*Minor differences ignored. Grouped by changes, with first version listed as example.
Not that I demand a gift. Again he repels an unfavourable opinion that might be formed of immoderate cupidity, that they might not suppose that it was an indirect hint,  as if they ought singly to stand in the room of all,  and as if he abused their kindness. He accordingly declares, that he consulted not so much his own advantage as theirs. "While I receive from you," says he, "there is proportionably much advantage that redounds to yourselves; for there are just so many articles that you may reckon to have been transferred to the table of accounts." The meaning of this word  is connected with the similitude formerly employed of exchange or compensation in pecuniary matters.
1 - "Pour les induire a continuer;" -- "To induce them to hold on."
2 - "Comme si eux deussent tenir la place de tous, et faire pour les autres;" -- "As if they ought to hold the place of all, and to act in the room of others."
3 - Calvin evidently refers to the word logon, (account,) which the Apostle had made use of in the fifteenth verse, in the phrase eis logon doseo; kai lepseo;, (in the matter of giving and receiving.) It is noticed by Beza, that the Rabbins make use of a corresponding phrase 'smv nchm (mattan umassa) -- giving and taking. -- Ed.
Not because I desire a gift - "The reason why I rejoice in the reception of what you have sent to me, is not that I am covetous." From the interest with which he had spoken of their attention to him, some might perhaps be disposed to say, that it arose from this cause. He says, therefore, that, grateful as he was for the favor which he had received, his chief interest in it arose from the fact that it would contribute ultimately to their own good. It showed that they were governed by Christian principle, and this would not fall to be rewarded. What Paul states here is by no means impossible; though it may not be very common. In the reception of layouts from others, it is practicable to rejoice in them mainly, because their bestowment will be a means of good to the benefactor himself. All our selfish feelings and gratifications may be absorbed and lost in the superior joy which we have in seeing others actuated by a right spirit, and in the belief that they will be rewarded. This feeling is one of the fruits of Christian kindness. It is that which leads us to look away from self, and to rejoice in every evidence that others will be made happy.
I desire fruit - The word "fruit" is often used in the Scriptures, as elsewhere, to denote results, or that which is produced. Thus, we speak of punishment as the fruit of sin, poverty as the fruit of idleness, and happiness as the fruit of a virtuous life. The language is taken from the fact, that a man reaps or gathers the fruit or result of that which he plants.
To your account - A phrase taken from commercial dealings. The apostle wished that it might be set down to their credit. He desired that when they came to appear before God, they might reap the benefit of all the acts of kindness which they had shown him.
Not because I desire a gift - I do not speak thus to incite you to send me a farther gift; I speak this on the general subject, because I wish you to bear such fruit as shall abound to your account in the day of the Lord.
(10) Not because I desire a gift: but I desire fruit that may abound to your account.
(10) He witnesses again that he admits well of their benefit, not so much for his own sake as for theirs, because they gave it not so much to him, as they offered it to God as a sacrifice, of which the Lord himself will not be forgetful.
Not because I desire a gift,.... This commendation of them he entered into, not because he desired another present to be made to him, either by them or others; he was not a man of such a disposition, he was not like one of those that could never have enough; he was fully satisfied and highly contented with what he had; he was not like the false teachers, that made merchandise of men; he sought not theirs, but them:
but I desire fruit that may abound to your account; he had planted them, or had been an instrument in planting of them, as trees of righteousness, Isaiah 61:3; and his great desire was to see fruits of righteousness grow upon them, Philippians 1:11; by which sometimes are meant acts of beneficence, as in 2-Corinthians 9:10; and that these might be abundant and turn to their profit and advantage, as such fruit does; for God does not forget to recompence acts of bounty, and labours of love, but if even a cup of cold water is given to a prophet or minister of Christ, on account of his being so, it shall have its reward in the issue of things, upon the casting up of accounts, Matthew 10:42; for the apostle still has reference unto that; his view was, that the balance might be on their side, and that much might be received by them; so that it was not for himself, but for their encouragement and future good, he said this; for as for himself he adds,
a gift--Greek, "the gift." Translate, "It is not that I seek after the gift, but I do seek after the fruit that aboundeth to your account"; what I do seek is your spiritual good, in the abounding of fruits of your faith which shall be put down to your account, against the day of reward (Hebrews 6:10).
Not that I desire - For my own sake, the very gift which I receive of you.
*More commentary available at chapter level.