Asset (15-16): Paul hinted at his desire to have Onesimus serve him in Rome (13-14), but he doesn't demand Philemon to grant him this. In His providence, God may bring about a different outcome. Onesimus may have run away so that Philemon may ultimately have him as a beloved brother.[1] With a Christian slave,[2] he wouldn't just have a man useful for service in the flesh[3] but for service in the Lord.[4] Onesimus is going to be a spiritual asset!
Partnership (17): Paul then makes his request known. Philemon is to treat Onesimus as he would treat the Apostle, as a partner in the faith. Paul is sure[5] they share in this partnership (another word for "fellowship") of believers (1:6). Besides this, Onesimus is now also a part of this fellowship (1 John 1:7). Believers' partnership with one another is real and practical, not theoretical.
Repayment (17-19): Paul also models this partnership himself. He will fully assume whatever debt Onesimus owed Philemon. And Paul is dead serious. He writes this promise of repayment with his own hand![6] Paul saw his material possessions rightly (Acts 2:45; 20:35) and loved people with his heart and his wallet! Philemon received such a love in the past. Now, he is to pay it forward.
[1] "Forever [ai-ōn-i-os (αἰώνιος)]" points to eternity. Spiritual brotherhood would remain unto eternal life.
[2] If Paul expected manumission, he would have incurred the payment for his freedom, not his debt. "No longer as [i.e., in the character of] a slave" points to Onesimus' greater value than a mere slave ("more than a slave"). Christian masters were not required to free their slaves, but to treat them well (cf. Eph. 6:9; Col. 4:1).
[3] Onesimus is expected to serve his believing master even more heartily as a Christian slave (cf. 1 Tim. 6:2).
[4] "In the flesh and in the Lord" modifies the main verb "have him back." Given the juxtaposition of slave and brother in this sentence, "in the flesh" best describes service as a slave and "in the Lord" Christian ministry.
[5] "If then you regard me" is a first class condition with the sense of "Since." Paul is sure of this relationship.
[6] Letters were often written with an amanuensis (Rom. 16:22; 1 Pet. 5:12). Paul habitually writes his own greetings (Col. 4:18; 2 Thess. 3:17). This is the only time when he inserts his own writing for a non-greeting.