Seems like alot of people here overvalue AK preflop and post flop. I will certainly lose alot on this board as well, but I wouldnt have played for my whole stack. Play for your whole stack when your the one with a set of dueces. With no reads, two pair is not worth losing your entire stack. Thats all I am saying. Bloating the pot up like this makes it impossible to get away from.

I personally would raise more like 4xBB preflop, then half the pot on the flop, then 3/4 on the turn if you put him on a draw. Then if he still calls and a blank comes, put in a good value bet on the river. If he comes over the top on the river he most likely has a slow played monster. AK should not be a losing hand, your doing something wrong obviously.

Also ask yourself what hands call your turn push that you can beat? You dont have enough reads to tell if villian would PF raise with AQ, so that is a possibility. With his range of cards, the only hand that I see him calling here that you have beat is AQ, some sort of monster draw, A6, A2.
I dont think most people are calling A6 or A2 to a preflop raise. You want him to have AQ really. He bet into a PF raiser that showed strength on the flop, that always smells fishy. The way villian played the hand was well because it looked like a good draw and I probably would have put him on a draw and donated my money to him.