50NL: AKs flop an Ace on a 3bet flop

Pacific Poker
No Limit Holdem Ring game
Blinds: $0.25/$0.5
5 players

MP ( $78.25 )
CO ( $127.56 )
Button ( $122.65 )
SB ( $57.74 )
BB ( $50.7 )

Converter

Pre-flop: (5 players) Hero is Button with A :spade: K :spade:
MP calls, CO folds, Hero raises to $2, SB folds, BB raises to $3, MP folds, Hero calls.

Flop: 2 :diamond: 4 :heart: A:club: ($6.75, 2 players)
BB bets $4.53, Hero calls.

Turn: 7 :diamond: ($15.81, 2 players)
BB bets $15.77, Hero ???.

villain was 68/29/2. This is a push, right? We are only behind to AA ...

This is not a 3bet pot, I don't care that there was a raise and reraise PF. A 3bet Pot at 50nl should have at least $12+ in it. As played, you can shove now.

I would 4-bet this preflop a lot.

As played I don't mind calling down and getting it in on the river. AJ, AQ will do the betting for you, and you might scare of KK- with a turn raise.

This looks like a very standard fistpump shove to me. You have le nuts.

4-betting PF is fine as well.

4-bet pre, shove over turn. If this was a proper 3-bet pot i would most likely shove over a flop bet.

Hmm it seems like I'm the only one calling the turn down as played. Am I too weak here? Are we pushing because of his betsize?

IMO pushing turn reveals our hand and makes it a bit easier for villain to get away.
If we call then villain is the one that needs to make a decision on the river. He's probably pushing his last 1/2PSB, maybe c/c KK or something.
I just think a bet on the river gets called more often than a turn raise.

4-bet this? I haven't thought about that ... I'll have to consider this on these stupid 3-bets!