400NL 6max: Push preflop vs a 2+2er?

[LuckyDice]

Villain in this hand is a 2+2er and is 21/15/2 over my almost 600 hands. His range to steal blinds is very wide, so my 3-betting range is pretty wide. I think he knows this, but this is the first time I've been 4-bet by him.

My image is pretty TAGish I'd imagine.

Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

MP ($320)
CO ($1448.95)
Button ($453)
SB ($351)
Hero ($485.80)
UTG ($721.50)

Preflop: Hero is BB with K[img]/images/graemlins/spade.gif[/img], A[img]/images/graemlins/club.gif[/img].
<font color="#666666">3 folds</font>, <font color="#CC3333">Button raises to $16</font>, <font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises to $58</font>, <font color="#CC3333">Button raises to $156</font>

I'd sorta expect him to just call with AA/KK, maybe even QQ/JJ but I'm not certain. So with all the money in the pot, is this a push or a fold?