Weeeeird spot with AK, all streets

[DJ Sensei]

10/20 6max, I'm in BB with A[img]/images/graemlins/diamond.gif[/img]K[img]/images/graemlins/diamond.gif[/img].

UTG (3900) - solid regular
MP (3800) - mostly unknown
CO (2000)
Button (2700) - mostly unknown
SB (4000)
Hero, BB (2000) - TAG image probably, but maybe unknown to these other guys

UTG: raises to $70
MP: raises to $220
CO: folds
Button: coldcalls
SB: folds
Hero: calls?
UTG: calls

Flop [ 5[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/club.gif[/img] 4[img]/images/graemlins/club.gif[/img] ] (Pot ~ $900)

Hero: checks?
UTG: checks
MP: checks
Button: checks

Turn [ 7[img]/images/graemlins/club.gif[/img] ] (Pot ~ $900)

Hero: checks?
UTG: checks
MP: checks
Button: bets $325
Hero: calls
UTG: folds
MP: folds

River [ 7[img]/images/graemlins/heart.gif[/img] ] (Pot ~ $1550)

Hero: checks (intending to call anything, probably)

I could see a preflop 4-bet or a turn and/or river bet as played being the most obvious alternatives to this line. just a weird spot all around. How would you play it?