Your call after the flop is the problem.
Having been hit by a raise after that flop, you've got to re-raise or fold.

Just my £0.02

why?

To find out where the villain's at, and to protect your AA (against e.g. villian hitting low pair, or chasing a straight).

hmm
if i were in this hand i would have done nearly all the same but the reraise on the river i wouldnt call because it seems like he wants a call.

A lot of ppl would raise the flop bet. I have two problems with the raise. 1. If he re-raises we have problems. 2. The pot size escalates and our hand isn't that good.

What hand do you put him on after the flop?

I'm not really sure I get your point Jules. Do you want us to say why we think it was badly played? What would we do instead and why? Or what?

Interested in your general thoughts on the hand, and the river bet in particular

Well my alarms would be set off at the flop for sure. BB bets out of position into a preflop raiser (although I was the button so he might have thought I was just stealing the blinds). By that time I would say him to have an ace. Why? His bet signifies he probably doesn't have a straight draw or a flush draw. He didn't re-raise me preflop so he probably doesn't have a good card (not really true I admit but I'm talking mainly about mid-high pocket pairs). And a low pair, whether it's sixes, threes or pockets, sounds like a too weak card to bet in such a way. So after the flop my guess would be he has an ace with a low-mid kicker at least. Depending on whether I'd read his profile as aggressive or tight I'd either raise (some $3 or so) or fold. Call in this case turned out to be the worst possible thing because that way I told him I din't have as strong card as I'd have liked. Which means he can keep pushing on turn and river and possibly make me fold without even seeing his cards.

The 2 on turn apparently didn't change anything so whatever reason made me call on flop would work here as well.

The valuebet on river was a weird decision though. If I was certain I had a better hand I would surely bet more - the opponent has shown a willingness to bet a lot throughout this game. Or I might have bluffed with an even higher bet (probably not in this case, especially against an almost twice the stack size). But most probably I would have just checked and hoped because by that time I would be quite certain I lost. Value bet in such a situation is just a waste of chips. It will certainly not scare him off cause of my calls on flop and turn.

However... we have a certain proverb in Czechia, it goes like this: "Po bitvě je ka¾dý generál", meaning Everyone's a general after the battle. So saying what I'd do knowing the outcome is quite easy...

Oh yeah, and damn you for making me go through the grammar tense hell. I hope it's as hard for you to read as it was for me to write. :P