This is a very good question. It is both minor and major. Minor in the sense that it was an early transgression that was caught, discussed and hasn’t recurred. It involved kissing and ended there. In the world of complicated and frustrating relationships, this has hope.
You have made your case and he has heard you. What have you got to lose by letting him prove to you he wants to be in a committed relationship? See how you feel. If, after a bit of time you can’t feel his sincerity, it is best to move on. But you have both done what would be needed to be done to heal a relationship. Give it some time and see if it does. If your heart and mind won’t allow it, it is time to move on. You both deserve to have a relationship that you feel good in.