Albert Barnes Commentary 2 Corinthians 13:3

"seeing that ye seek a proof of Christ that speaketh in me; who to you-ward is not weak, but is powerful in you:" — 2 Corinthians 13:3 (ASV)

Since you seek a proof of Christ speaking in me. See Barnes on previous chapters. They had called his apostolic authority into question; they had demanded evidence of his Divine commission. He says that he would now furnish such evidence by inflicting just punishment on all offenders, and they would then have abundant proof that Christ spoke by him, or that he was inspired.

Which toward you is not weak. Or, this refers to Christ, who is not weak toward you. Christ has manifested his power abundantly toward you; that is, either by the miracles that were performed in his name; by the diseases and calamities which they had suffered on account of their disorders and offenses (see Barnes on 1 Corinthians 11:30, and on 1 Corinthians 5:1 and following); or by the force and efficacy of his doctrine.

The connection, it seems to me, requires that we should understand this as referring to the calamities inflicted by Christ on them for their sins—calamities which Paul says would be inflicted again if they did not repent. The idea is that they had already received ample demonstration of Christ’s power to inflict punishment, and they had reason to apprehend it again.