9 Yet for love's sake I rather beseech thee, being such an one as Paul the aged, and now also a prisoner of Jesus Christ.
[AD 420] Jerome on Philemon 1:8-9
I am writing to you because of the confidence I have in Christ Jesus, commanding you to do what is proper for the sake of love. I urge you even more, as one such as Paul, an old man and now also a prisoner of Christ Jesus. With many praises given to Philemon before him, considering the matter at hand, which would be both excellent and helpful to the requester, Paul was able to command rather than request. And this confidence came from the fact that whoever had done such great works for Christ could not be unequal to himself in other aspects. But he wishes to ask more than to command, with the authority of one asking for something great being proposed, through which both the Apostle begs, and the old man and prisoner of Jesus Christ. But that for which he is asking the whole time is: Onesimus, the servant of Philemon, he had fled and compounded some domestic item by theft: hence he had gone to Italy, so that he would not be easily apprehended in the near future, he had squandered his master's money through luxury. Lest anyone think this rashly, and that it is made up as we please, let him learn in the following. For Paul would never say: "If he has harmed you or owes anything, put it to my account: I, Paul, have written with my own hand; I will repay it." Nor would he become the surety of a lost thing, and if that which was lost had not been squandered. Therefore, when Paul was in prison in Rome because of the confession of Christ, he believed in Christ; and after being baptized by him, he wiped away the stains of his former life with worthy penance, to such an extent that the apostle himself became a witness of his conversion, who had once rebuked Peter for not walking rightly in the truth of the Gospel (Galatians 2). Therefore regarding sin and wrongdoing, in which he had injured the lord, he doesn't deserve forgiveness; however, regarding the testimony of the Apostle, who knows that he has been fully converted, he is burdened with great weight, since he is being asked who was once a fugitive slave and a robber, yet had become a minister of the Apostle. (And what other ministry does the Apostle have except the Gospel of Christ Jesus?) Now he is no longer to be forgiven as if by his master, but rather as if by a fellow servant and co-evangelist, as he too is a servant of Christ and a minister.

[AD 384] Ambrosiaster on Philemon 1:9
Paul makes an appeal for him. Philemon was about the same age as Paul and also a 'prisoner' of Jesus Christ, which means that he was obliged to do the Lord's buisness or even subject to imprisonment on account of the name of Christ, as the apostles themselves also were.
[AD 397] Ambrose of Milan on Philemon 1:9
He desired Philemon to imitate not his youth but his old age. (On Joseph)
[AD 407] John Chrysostom on Philemon 1:9
Ver. 9. "Yet for love's sake, I rather beseech you."

As if he had said, I know indeed that I can effect it by commanding with much authority, from things which have already taken place. But because I am very solicitous about this matter, "I beseech you." He shows both these things at once; that he has confidence in him, for he commands him; and that he is exceedingly concerned about the matter, wherefore he beseeches him.

"Being such an one," he says, "as Paul the aged." Strange! How many things are here to shame him into compliance! Paul, from the quality of his person, from his age, because he was old, and from what was more just than all, because he was also "a prisoner of Jesus Christ."

For who would not receive with open arms a combatant who had been crowned? Who seeing him bound for Christ's sake, would not have granted him ten thousand favors? By so many considerations having previously soothed his mind, he has not immediately introduced the name, but defers making so great a request. For you know what are the minds of masters towards slaves that have run away; and particularly when they have done this with robbery, even if they have good masters, how their anger is increased. This anger then having taken all these pains to soothe, and having first persuaded him readily to serve him in anything whatever, and having prepared his soul to all obedience, then he introduces his request, and says, "I beseech you," and with the addition of praises, "for my son whom I have begotten in my bonds."

Again the chains are mentioned to shame him into compliance, and then the name. For he has not only extinguished his anger, but has caused him to be delighted. For I would not have called him my son, he says, if he were not especially profitable. What I called Timothy, that I call him also. And repeatedly showing his affection, he urges him by the very period of his new birth, "I have begotten him in my bonds," he says, so that on this account also he was worthy to obtain much honor, because he was begotten in his very conflicts, in his trials in the cause of Christ.

[AD 407] John Chrysostom on Philemon 1:9
Paul appeals to Philemon on a number of grounds: the quality of his person, his age, because he was old, and from what was more just than all, because he was also a “prisoner of Jesus Christ.”

[AD 428] Theodore of Mopsuestia on Philemon 1:9
Paul shows here what power his name alone has.

[AD 435] John Cassian on Philemon 1:9
You see how he rejoiced in the dignity of his chains, by the example of which he actually stirred up others. But there can be no doubt that where there is single-minded love of the Lord, there is also single-minded delight in chains worn for the Lord’s sake: as it is written: “But the multitude of the believers was of one heart and one soul.”
[AD 1107] Theophylact of Ohrid on Philemon 1:9
If dear, he will forgive; if a fellow-worker, he will not retain the slave, but will send him back for the ministry of preaching.
[AD 1274] Thomas Aquinas on Philemon 1:9
There are two things on account of which one ought to plead. Because of old age. 1 Timothy 1: ‘Do not reproach an old man, but ask him as a father.’ Again, because of the honourableness of virtue, for where we are not deficient, we are equals. Sirach 32:1, ‘Have they made you ruler? Be not lifted up: be among them as one of them.’ Therefore he says, since you are such as you are, as Paul, an old man, as if to say, if you were a boy, I would demand this of you, but you too are old. You are of the same stage of life as I. Not that they are such and so much simply speaking, but in a way similar, which he says out of his humility. Romans 12:10: ‘anticipating one another with honour’. Origen said that it is rare to find a useful teacher in the Church who is not old, thinking of Peter and Paul.