My take is, your guy is very insecure. If he can't get constant feedback (via your jealousy) proving your affection for him, he withdraws and sulks. It is not likely that anything you say or do is going to give him the self-esteem he obviously lacks; this has to come from within.
Can you stop reacting with jealousy and hurt when he teases you in this way? That would deprive him of the feedback he's craving, and possibly minimize his hurtful comments.
In my experience, it is a mistake to continue in a relationship with the hopes that your partner will change. People usually don't. I think you need to ask yourself if you can live with his behavior, or if it causes you more distress than joy. Believe me, it is easier to make this choice when you are a couple of years into the relationship, as opposed to a couple of decades.