Pre: Gotta raise. He's possibly raising with AQ, 55-JJ here, maybe KQ AJ sooted. So I would raise without a doubt, but thats my choice on how I play AK early in tournies.

Flop: Given how i said to play pre, I would lead out a standard c-bet and hope he calls. Given your check, i would have checked-raised here. The overbet doesn't seem like a set to me, and screams of weak ace.

Turn: In my senario, we're assuming he calls the flop, then i lead out the turn. Same if he calls a check-raise. How you played it, it's push/fold senario. You have no other bet on the River so you might as well get all the folding equity you can here on the turn.

River: In your case, you backed yourself into a blind spot, betting into someone with your last chips having no idea what they have.

By staying more agressive you can learn more information that will be more valuable on later streets, instead of trying to extract more value by slow playing a medium strength hand.