Jamieson, Fausset and Brown on Philemon 1:16

16. No longer as a mere servant or slave (though still he is that), but above a servant, so that thou shalt derive from him not merely the services of a slave, but higher benefits: a servant "in the flesh," he is a brother "in the Lord."

beloved, specially to me--who am his spiritual father, and who have experienced his faithful attentions. Lest Philemon should dislike Onesimus being called "brother," Paul first recognizes him as a brother, being the spiritual son of the same God.

much more unto thee--to whom he stands in so much nearer and more lasting relation.