AK 4-bet gets flat called

[blah-blah-blah]

villian is a regular running 23.4/20.9/4.2 over 160. I played with him at 200NL as well where he ran tighter at 19/16 over 250 hands. he seems pretty straightforward and I don't remember him doing anything out of line.

PokerStars No-Limit Hold'em, $4 BB (6 handed) pokerhand.org hand converter

Button ($401.15)
SB ($396)
BB ($545)
UTG ($409.40)
Hero ($470.35)
CO ($201.40)

Preflop: Hero is MP with K[img]/images/graemlins/spade.gif[/img], A[img]/images/graemlins/heart.gif[/img].
<font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises to $16</font>, <font color="#666666">1 fold</font>, <font color="#CC3333">Button raises to $52</font>, <font color="#666666">2 folds</font>, <font color="#CC3333">Hero raises to $112</font>, Button calls $60.

Flop: ($230) T[img]/images/graemlins/club.gif[/img], T[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, Button checks.

Turn: ($230) 2[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, Button checks.

River: ($230) 6[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets $134</font>, Button folds.

Final Pot: $364

I guess I should bet the flop? I thought KK/QQ would just shove pre and I can't see him flatting a 4-bet w/ JJ. if he has AK/AQ money should get in no matter what so I figured I'd check to give him a chance to hand himself? since I checked the flop should I be checking turn and river?

[Borned_Luckbox1]

I think, if you want to get called by KK/QQ you should just shove flop.

edit: or underbet

[Terrabon98]

underbet flop