What I'm about to write may sound harsh, but it comes from experience and learning the hard way. I think the issue goes deeper than food. You are teaching your son a way of relating and getting what he wants by manipulation and trying to make you feel bad. This will extend out in the world and he will act this way with others, who may or may not put up with it with consequences that I am sure you don't wish for him. If he is overweight already, you are not doing him any favors in the long run by keeping high calorie/fat foods in the house, but making him happy in the moment and relieving you of being the 'bad guy'.

This may or may not apply to you, so if it doesn't, call me nasty names and forget this post , but, I was a single parent for 7 years before I married my husband. My child has special needs, and because of some pretty heavy guilt that I felt (too long a story for this forum) I unwittingly gave in to a lot of his demands and taught him to manipulate me into giving him what he wanted. It took some 'heavy lifting' to change the way I parented and there were some rough patches when he realized (he is now almost 14) he could no longer demand or push me around, but he is a better and nicer human being for it. I still catch myself now and then slipping back into old patterns but overall, things are happier, and I am stronger. I know it is not easy, in fact it can be mind numbingly hard in a way that only someone who has been there can understand. I wish you all the best, you deserve to be treated with love and respect by your child, but he has to learn that from you and how you allow him to treat you.

p.s. if it's not in the house, it won't get eaten
p.s.s. child services never took a child from the home because there were no doughnuts