I had a boyfriend like that. If I got upset he would say "I'm just kidding!"
One day I said "Why do you think it is okay to kid around with me like that?"
I can't recall ever seeing a situation where I thought someone really was being too sensitive when hurt by a joke. It's just a poor excuse for the "jokes yet" to be passive aggressive. The phrase "I was just kidding!" to me is code for "I want to be hurtful to you under the guide of humor."