Can I ask to be reimbursed for his food?
Did you pay for his food?
No, but he doesn't know that.
Since you never paid for his food in the first place, asking him to pay you back is incorrect because it is stealing. Don't ask for recompense for something you never paid for in the first place.
I'm going to keep asking him to pay me
I think that you understand how wrong this is, and if you don't then let me ask you a question: How would you feel if someone was getting food for free and then making you pay for it? If you care about this person at all, then you shouldn't force them to spend money they don't have to.