Septuagint (LXX):   kai eipen (3SAAI) o agchisteus ou dunesomai (1SFMI) agchisteusai (AAN) emauto mepote diaphtheiro (1SPAI) ten kleronomian mou agchisteuson (2SAAM) seauto ten agchisteian mou hoti ou dunesomai (1SFMI) agchisteusai (AAN)
Click here for explanation of verb parsing abbreviations in parentheses after each verb

AND THE CLOSEST RELATIVE SAID I CANNOT REDEEM IT FOR MYSELF LEST I JEOPARDIZE MY OWN INHERITANCE:

"I will redeem it" quickly changes to "I cannot redeem it" when the reality of his responsibility for Ruth came to light. He experiences a "sudden" change of heart. Note also that the "go'el" uses a form of the Hebrew verb ga'al five times in one sentence! The nearest kinsman in not choosing to redeem Ruth passes off the pages of history anonymously!

Note that "closest relative" and "redeem" are the same word (01350) (ga'al) (click for word study of ga'al and go'el) is a verb in the Hebrew which has an active participle, Go'el, (which is usually translated as a noun = kinsman, redeemer, avenger). As stated earlier the TWOT states that Geullah is the  passive participle of ga'al, and is translated here and in Ruth 4:7 as "redemption".

As the TWOT states

The participial form of the Qal stem of the verb has practically become a noun in its own right though it may properly be considered as merely a form of the verb. (Harris, R. L., Harris, R. L., Archer, G. L., & Waltke, B. K. Theological Wordbook of the Old Testament Moody Press) 

The basic idea is to redeem or do the part of a kinsman and thus to redeem a kin from difficulty or danger.

"Jeopardize" (07843) (shachath/shahat)  means  to spoil, to ruin, to destroy, to pervert, to corrupt, to become corrupt, to wipe out. Shachath is used 3 times by Moses to describe the condition of the world in the days of Noah which was the reason God sent the worldwide flood...

Now the earth was corrupt (shachath/shahat) in the sight of God, and the earth was filled with violence. And God looked on the earth, and behold, it was corrupt (shachath/shahat); for all flesh had corrupted (shachath/shahat) their way upon the earth. (Genesis 6:11-12)

This verb describes what God did to wicked Sodom and Gomorrah...

And Lot lifted up his eyes and saw all the valley of the Jordan, that it was well watered everywhere-- this was before the LORD destroyed (shachath/shahat) Sodom and Gomorrah-- like the garden of the LORD, like the land of Egypt as you go to Zoar. (Genesis 13:10)

Jeopardize is translated in the Septuagint using the Greek verb diaphtheiro, (1311) (from dia = intensives the meaning of verb + phtheiro = to shrivel, destroy, defile) which means to cause the complete destruction of something. It conveys the idea of something that is utterly corrupted and gives us our English word for the deadly disease known as "diphtheria"!  The kinsman redeemer is concerned that to fulfill the role of the goel might "utterly corrupt" his estate, for he would have both Naomi and Ruth to support. Furthermore he did not want the field to be inherited by Ruth’s future son instead of members of his own family.

The Wycliffe Bible Commentary explains the goel's quick change of heart, writing that

"This would involve financial loss to the purchaser. The prospective goel would mar his own inheritance by spending money on land that would belong not to him but to a son of Ruth. The Targum suggests that the relative was already married, but this would not have relieved him of obligation." (Pfeiffer, C F: Wycliffe Bible Commentary. 1981. Moody)

If he had a son by Ruth, and that son were his only surviving heir, Mahlon’s property and part of his own estate would go to Elimelech’s family. The fact that Ruth was a Moabitess may also have been a problem to him. (Both Mahlon and Chilion had married Moabite women and died!) Boaz was undoubtedly relieved when his relative stepped aside and opened the way for Ruth to become his wife.

Jamieson explains it this way...

This consequence would follow, either, first, from his having a son by Ruth, who, though heir to the property, would not bear his name; his name would be extinguished in that of her former husband; or, secondly, from its having to be subdivided among his other children, which he had probably by a previous marriage. This right, therefore, was renounced and assigned in favor of Boaz, in the way of whose marriage with Ruth the only existing obstacle was now removed. (Ruth 4)

The Targum may give the proper sense of this passage (although it is still conjectural because there is no specific statement regarding his marital status):

"I cannot redeem it, because I have a wife already; and it is not fit for me to bring another into my house, lest brawling and contention arise in it; and lest I hurt my own inheritance. Do thou redeem it, for thou has no wife; which hinders me from redeeming it."

REDEEM IT FOR YOURSELF YOU MAY HAVE MY RIGHT OF REDEMPTION FOR I CANNOT REDEEM:

"Redeem it for yourself" (ga'al ) is in the imperative mood (command) and in the Hebrew sentence is in the emphatic position, and so reads

"redeem for you, you, my right of redemption".

The redeemer must not only be a kinsman, must be willing and must have the means to pay the redemption price.

Right of redemption (01353) (geullah) is given a Strong's number different than (ga'al) (01350) but both Strong's definition and the respected Theological Wordbook of the Old Testament that geullah (or ge'ulla) is a feminine passive participle of ga'al and functions as a feminine noun in the Hebrew. Don't let this technical explanation sidetrack you from the essence of the meaning of this word geullah, which expresses the action of a relative in setting free a member of his family or buying back his property (geullah is found in Leviticus 25:24:26, 25:29, 25:31-32, 25:48-49, 25:51-52) or in general that of purchasing something for a price. A ransom-price is paid to secure the release of what would otherwise be under forfeit.

The nearest kinsman's refusal to assume the role of kinsman-redeemer serves to further highlight the kindness and generosity of Boaz toward the two widows, even as as the Moabitess Orpah’s return to her pagan family highlighted Ruth’s selfless devotion and loyalty to Naomi.

John MacArthur explains that...

He was unwilling to have the family portfolio split between his existing children and the potential offspring of a union with Ruth. (MacArthur, J.: The MacArthur Study Bible Nashville: Word Pub)

When the go'el says "I cannot" is for all practical purposes saying "I will not". Lest we be to hard on the go'el, we need to be reminded that as believers we often take the same tact when confronted with a "pet sin" that we really don't want to be set free from -- we say "I cannot stop" when what we really mean to say is "I will not stop".

In fairness, it should also be mentioned that some commentators feel that the reason the nearest kinsman said "I cannot" is that if he paid the price for the land, and took on the added expense of caring for a wife, he would be overextended financially.

The Bible Knowledge Commentary explains that...

Perhaps he was too poor to sustain the land and a wife. Or, as some have suggested, perhaps he feared to marry a Moabitess lest the fate of Mahlon, Ruth’s first husband (Ru 4:10), befall him. Perhaps the best view is that when he learned from Boaz that Ruth owned the property along with Naomi (Ru 4:5), he knew that if Ruth bore him a son, that son would eventually inherit not only the redeemed property but probably part of his own estate too. In that sense the nearer redeemer would “endanger” his estate. However, if only Naomi were the widow (not Naomi and Ruth), then no son from the levirate marriage would inherit part of the redeemer’s estate because Naomi was past childbearing. (Walvoord, J. F., Zuck, R. B., et al: The Bible Knowledge Commentary. 1985. Victor).

Believer's Study Bible says that...

Boaz was bringing together two originally separate obligations: (1) buying the land of Naomi (Lev. 25:25-28), and (2) marrying Ruth to perpetuate the inheritance of Mahlon (Deut. 25:5-10; Num. 27:9-11). This was too difficult for the nearer kinsman, but Boaz was able. (Criswell, W A. Believer's Study Bible: New King James Version. 1991. Thomas Nelson)

A G Auld has a thought provoking common by way of application writing that...

Service beckons—and we do not know whether it is an opportunity or an obligation. Our excuses are often expressed in terms of solemn undertakings already given such as our family commitments. “I cannot...lest I impair my own inheritance.” Those who seek to shape their lives by the gospel tradition must remember the several sayings which warn against giving the family an ultimate veto. Jesus talks of those who have left house or brothers or sisters or mother or father or children or land for his sake and for the gospel (Mark 10:29); and he also notes that “Whoever does the will of God is my brother, and sister, and mother” (Mark 3:35). Christians may not readily think of themselves as sharing in the responsibility of redemption. Yet solidarity with brother and neighbour is precisely our calling—with brothers who are not of our own family, and with neighbours who are far from our own doors. (Auld, A. G. (2001, c1984). Joshua, Judges, and Ruth. The Daily study Bible series (276). Louisville: Westminster John Knox Press)

Warren Wiersbe applies this teaching on redemption to believers writing that...

Septuagint (LXX):   kai touto to dikaioma emprosthen en to Israel epi ten agchisteian kai epi to antallagma tou stesai (AAN) pan logon kai hupelueto (3SIMI) o aner to hupodema autou kai edidou (3SIMI) to plesion autou to agchisteuonti (PAPMSD) ten agchisteian autou kai touto en (3SIAI) marturion en Israel 

"This is the way it used to be in Israel concerning buying back property and exchanging goods:" (GWT)

Note that "the custom" is not present in the original Hebrew text but is added by the translators, which is certainly reasonable in light of the fact that the Septuagint translation literally renders it "the ordinance (1345) (dikaioma) in Israel for redemption". The Greek word dikaioma is derived from dike = right and means primarily that which is deemed right, so as to have the force of law; hence an ordinance (an authoritative decree or direction, a law set forth by a governmental authority).

Redemption (01353) (geullah) is a feminine passive participle of ga'al and functions as a noun in the Hebrew expressing the action of a relative in setting free a member of his family or buying back his property that had been sold for debt. The law required that the "right of redemption" of land and of persons be protected (geullah is used with this meaning in Leviticus 25:24:26, 25:29, 25:31-32, 25:48-49, 25:51-52). A ransom-price is paid to secure the release of what would otherwise be under forfeit.

TO CONFIRM ANY MATTER A MAN REMOVED HIS SANDAL AND GAVE IT TO ANOTHER AND THIS WAS THE MANNER OF ATTESTATION IN ISRAEL: 

"In order to make every matter legal, a man would take off his sandal and give it to the other man. This was the way a contract was publicly approved in Israel." (GWT)

Attestation (08584) (te'uwdah/te'uda) was a method of legalizing transactions, and formally was a testimony, an act. of making a binding agreement.

Deut 25:7-10 states that

"if the man does not desire to take his brother’s wife, then his brother’s wife shall go up to the gate to the elders and say, ‘My husband’s brother refuses to establish a name for his brother in Israel; he is not willing to perform the duty of a husband’s brother to me. “Then the elders of his city shall summon him and speak to him. And if he persists and says, ‘I do not desire to take her,’ then his brother’s wife shall come to him in the sight of the elders, and pull his sandal off his foot and spit in his face; and she shall declare, ‘Thus it is done to the man who does not build up his brother’s house.’ “And in Israel his name shall be called, ‘The house of him whose sandal is removed.’

The exact explanation of the shoe removal in the overall transaction is not entirely clear and the following comments are somewhat conjectural in the absence of clear Scriptural guidelines. Clearly the exact practice described in (Deut 25:7-10) was not invoked in the current transaction between Boaz and the nearer goel. Instead of the woman taking off her shoe and spitting in the face of the man who refused to be her goel, here we see one of the two men pluck off his shoe, and give it to the other man. Presumably the man who took off his shoe renounced any legal rights he had in the matter, and thus symbolically transferred ownership. A similar custom is mentioned in the Nuzu tablets. This practice of taking off one's shoe may relate to the divine commandment to walk on the land and take possession (Ge 13:17; Dt. 11:24; Josh. 1:3). The the passing of the sandal may have symbolized Boaz’s right to walk on the land as his property. The closer relative legally transferred his right to the property as symbolized by the sandal, most likely that of the nearer relative, although the text does not state who took the sandal off!

Warren Wiersbe comments that on the shoe removal that

Septuagint (LXX): kai eipen (3SAAI) o agchisteus to Boos ktesai (2SAMM) seauto ten agchisteian mou kai hupelusato (3SAMI) to hupodema autou kai edoken (3SAAI) auto 

"Closest relative" is again the verb (01350) (ga'al).

"Buy" (07069) (qanah) (in the form of an imperative or a command) means to buy, to purchase, to acquire, to possess. This is the very word used to describe God Himself "buying back" His people...

"Terror and dread fall upon them; By the greatness of Thine arm they are motionless as stone; Until Thy people pass over, O LORD, Until the people pass over whom Thou hast purchased (qanah)." (Exodus 15:16)

"Remember Thy congregation, which Thou hast purchased (qanah) of old, which Thou hast redeemed (ga'al) to be the tribe of Thine inheritance; And this Mount Zion, where Thou hast dwelt." (Psalm 74:2)

Then it will happen on that day that the Lord will again recover (qanah) the second time with His hand The remnant of His people, who will remain, From Assyria, Egypt, Pathros, Cush, Elam, Shinar, Hamath, And from the islands of the sea. (Comment: Refers to a yet future regathering of the Jewish people at the second coming of Christ -- Matt. 24:31-- the first being the regathering under Zerubbabel in 537 B.C.)

God did Boaz the honor to bring him into the line of the Messiah, while the kinsman, who was afraid of lessening himself, and marring his inheritance, has his name, family, and inheritance forgotten.

"Removed his sandal"

The IVP Background Commentary has the following note of explanation regarding the sandal scene: