How often do you push AK heads up, even when stacks are deep? I think AK is a good push hand, because many times you get called with A9-AQ or at worst you're flipping, unless dominated by AA KK. You will miss the flop 2/3 of the time, so is pushing better?

For example: We have been playing for about 8 mins now. Villian does not respect my pf raises at all and will call with almost any 2. If I raises and miss the flop, what can I put him on? He has been calling down bets with midpair, sometimes even worse. I am in the "wait for a hand" mode because this is how you usually break these kind of players.. but how I get value from AK here?

PokerStars No-Limit Hold'em Tourney, Big Blind is t20 (2 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

givememyleg (t1340)
Button (t1660)

Preflop: givememyleg is BB with A, K.
Button calls t10, givememyleg raises to t100, Button calls t80.

Flop: (t200) 8, J, 4 (2 players)
givememyleg checks, Button bets t80, givememyleg raises t220, Button calls t140.

Turn: (t640) 4 (2 players)
givememyleg ????????

I don't think I played this great, I think I should have Cbet... but lets say I had Cbet out and get flat called, then what on the turn?

-----

Another Example:

PokerStars No-Limit Hold'em Tourney, Big Blind is t30 (2 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

givememyleg (t1255)
BB (t1745)

Preflop: givememyleg is Button with A, K.
givememyleg raises to t90, BB raises to t180, givememyleg raises to t1255, BB calls t1075.

Flop: (t2510) 7, 2, 5 (2 players)

Turn: (t2510) 6 (2 players)

River: (t2510) 7 (2 players)

Final Pot: t2510

Stacks are still very deep in accordance to blinds... is this push unnecessary? After playing with him for about 15 mins, I have on a range to call with 66+, A9+, or any 2 broadway cards. This makes my FE pretty low, but I could be in a good spot.

If I had to sum up this whole mess into one question, is it better to push harder preflop when heads up with hands like AQ, AK.. esspecially when villian calls standard raises with any 2 cards preflop?