[StellarWind]

Cap preflop or checkraise the flop.

There are several good strategies for capping preflop when headsup, but I believe that autocapping AA-QQ, AK, possibly AQ, and no others is not one of them versus a sentient opponent. The 2+2 forums' standard dogmatic advice on capping doesn't actually make any sense unless you like playing with your hand face up.

You have a lot of pot equity so the flop 3-bet is OK but only if you intend to bet the turn and try to drive him off another AK. Getting raised on the turn is not so bad because at least you now know you don't need to call the river when you whiff.

It's dangerous to make sweeping judgments based on one hand, but I'm sure what I'm about to say applies to someone who is reading this so it won't be a waste.

The turn is the second street in a row where you made a play that has no obvious connection to the previous street. One of my current self-improvement areas is thinking about poker hands as a whole and developing appropriate strategies that address the whole hand. Calling the preflop 3-bet is fine if it's part of an actual plan that addresses likely postflop scenarios. It's less good if you just made it up and have no idea what comes next. 3-betting the flop is OK if it's part of a plan like stealing the pot or value betting the best hand (it's possible, there are certain Villains that only raise to bluff in this situation). But 3-betting the flop and checking the turn says to me that there was no plan and you effectively started over when the blank turn hit.

Note that this type of hand planning is pretty strictly advance preparation. Only a few rare talents improvise well without having done their homework.