I probably would have stayed weak on the river (either continuation 15 bet or check) and hoped to call a weak raise.

One more think, sometimes your Aces are going to be busted up. I'm not saying that its not possible to save a few bucks on this hand, but if you post a HH w/ busted Aces, you will always get a bunch of theories on how you could save the money.

To me, it looks like this guy flopped a set, got a dream turn card, and made a bunch of money, just like you would expect against AA.