Albert Barnes on 2 Corinthians 13:9

For we are glad, when we are weak, etc. We rejoice in your welfare, and are willing to submit to self-denial and to infirmity, if it may promote your spiritual strength. In the connexion in which this stands it seems to mean, "I am content to appear weak, provided you do no wrong; I am willing not to have occasion to exercise my power in punishing offenders, and had rather lie under the reproach of being actually weak, than to have occasion to exercise my power by punishing you for wrong-doing; and provided you are strong in the faith and in the hope of the gospel, I am very willing, nay, I rejoice that I am under this necessity of appearing weak."

And this also we wish. I desire this in addition to your doing no evil.

Even your perfection. The word here used occurs nowhere else in the New Testament, though the verb from which it is derived (καταρτιζω) occurs often, Mt 4:21, 21:16, Mk 1:19, Lk 6:40, Romm 9:22, 1Cor 1:10 2Cor 13:11, Gal 6:1, 1Thes 3:10, et al. 2Cor 13:11. On the meaning of the word, see Rom 9:22. The idea of restoring, putting in order, fitting, repairing, is involved in the word always; and hence the idea of making perfect--i, e., of completely restoring anything to its proper place. Here it evidently means that Paul wished their entire reformation--so that there should be no occasion for exercising discipline. Doddridge renders it, "perfect good order." Macknight, "restoration." For this restoration of good order Paul had diligently laboured in these epistles; and this was an object near to his heart.

(b) "even your perfection" 1Thes 3:10, Heb 6:1