OK, I’m pretty damn sure this isn’t by Stephen King. I’ve trawled through all the relevant Wikipedia entries on his works and I’ve googled the heck out of what I can recall and I’ve come up with zip. It sounds a little like Thinner, but that’s a novel, I’ve read it, and it isn’t this short story.
The basic idea of the story is that a fat guy is desperate to lose weight, so he gets a magic invisible monkey to ride on his back and eat all of the food he attempts to eat. The monkey, of course, gets fat and aggressive as time goes on, growing to substantial proportions while the guy wastes away. He finds out he can eat by fooling the monkey, like by dunking his head into a bowl of cereal before the monkey can stop him. This enrages the monkey and causes it to beat him about the head and neck.
I don’t remember how it ends. I probably read this about a decade ago now, likely checked out from a library then, so put it at 15 years old now at a minimum. I’m also pretty damn sure it was a short in a collection, but I could be wrong; I can plow through novels pretty fast when I want to.