Jamieson, Fausset and Brown on 2 Corinthians 2:9

9. For--Additional reason why they should restore the offender, namely, as a "proof" of their obedience "in all things"; now in love, as previously in punishing (2Co 2:6), at the apostle's desire. Besides his other reasons for deferring his visit, he had the further view, though, perhaps, unperceived by them, of making an experiment of their fidelity. This accounts for his deferring to give, in his Epistle, the reason for his change of plan (resolved on before writing it). This full discovery of his motive comes naturally from him now, in the second Epistle, after he had seen the success of his measures, but would not have been a seasonable communication before. All this accords with reality, and is as remote as possible from imposture [Paley, Horæ Paulinæ]. The interchange of feeling is marked (2Co 2:4), "I wrote ... that ye might know the love," &c.: here, "I did write, that I might know the proof of you."