Albert Barnes on 2 Corinthians 2:8

Wherefore I beseech you that ye would confirm your love toward him. The word here rendered confirm, (κυρωσαι) occurs in the New Testament only here and in Gal 3:15. It means, to give authority, to establish as valid, to confirm; and here means that they should give strong expressions and assurances of their love to him; that they should pursue such a course as would leave no room for doubt in regard to it. Tindal has well rendered it, "Wherefore I exhort you that love may have strength over him." Paul referred doubtless, here, to some public act of the church by which the sentence of excommunication might be removed, and by which the offender might have a public assurance of their favour.