Jamieson, Fausset and Brown on 2 Corinthians 2:10

10. Another encouragement to their taking on themselves the responsibility of restoring the offender. They may be assured of Paul's apostolic sanction to their doing so.

for if I forgave anything, to whom I forgave it--The oldest manuscripts read, "For even what I have forgiven, if I have forgiven anything."

for your sakes forgave I it--He uses the past tense, as of a thing already determined on; as in 1Co 5:3, "I have judged already"; or, as speaking generally of forgiveness granted, or to be granted. It is for your sakes I have forgiven, and do forgive, that the Church (of which you are constituent members) may suffer no hurt by the loss of a soul, and that ye may learn leniency as well as faithfulness.

in the person of Christ--representing Christ, and acting by His authority: answering to 1Co 5:4, "In the name of our Lord Jesus Christ ... my spirit, with the power of our Lord Jesus Christ."