I think the odds that your AA will hold up are pretty good

Very true, you are the big favorite. The issue is if they hold up you're not going to make any money (again, barring a perfect flop, say A rag rag and he pairs 2 rags) but you will lose a lot of money if he hits the flop. You're giving implied odds on your whole stack, he is giving you no odds. You're taking the worst of it here unless you re raise most of the time.

Now IF you re raise, and the board comes Q72r or something, that's a flop I might slow play hoping he would continue bet, you're not nearly as scared of rags after he called the raise. Regardless I'm 'coming out of the woods' on the turn, unless the turn makes me a set.... even then assuming a flush draw gets there I'm probably leading out. At that point the guy either has hand he's going to pay you with or not.