Hmmm...........well 22 or JJ is what we're worried about (33 less likely given there are two 3's out there now)
Villians min checkraise on the flop is pretty retarded, generally I assume someone is a wicked n00b when they make this play.
Granted, he could be banking you're on KK/AA and can't get away from it. But he could also have AJ, KJ, etc.
If he flopped a set why is he going to make it so cheap for you on the flop to outdraw him?
Not to mention you half-potted on a relatively dry board, so he could be thinking you're on a whiffed AK and that you can't stand anymore action unless you have the A

K
Then when you call his flop minraise and he sees a safe turn card, he likely fears you have the flush draw and doesn't want you to see the river for free.
Since you didn't repop him on the flop your AA is underrepped here and he likely thinks his Jack is good.
I think our Aces are good here, although if you have a tell that leads you to believe otherwise, go with your feelings, you obviously have a ton more experience than us.