[Moozh]

Of course you don't fold to a 3-bet. When I miss with AK heads-up, I vary on a flop raise for a free card and a flop raise-turn bet. The line I take depends on the opponent. Because this guy looks to be the passive type, I'm giving him credit for a pair here. Since he's on the loose side of things, I'm not going to try and bet him off his hand. On top of that, passive players are willing to slow down to aggression much more quickly, increasing the chance that the free-card play will be successful.

So, I choose the free card play because:

1) His bet into me on the flop after my pre-flop raise makes me think I'm behind.
2) Because he is loose-passive, I don't think I can make him fold his pair.

Now, if you do want to go to a showdown with him unimproved, you still need to raise the flop. After that, I'm fine with the bet going in on either the turn (betting for a free showdown) or the river (taking the free card and calling the river unimproved). Either of those two will get you to a showdown for 4 small bets. Calling down costs you 5.

Oh, and if he 3-bets me on the flop I call the flop, call the turn, and fold the river unimproved.