KK in 4bet pot but unhappy on the flop...

[Vinland]

Big hand for me. Unfortunately I don't know how to pose the question without possibly giving some leading information away.

Villain was 9/4/3.6 over 405 hands.
Very tight player and he plays straight forward imo. Doesnt really get out of hand or play tricky. Shows down pretty strong hands.
His limp reraise was strange...doesnt happen very often. I was playing tight as well around 12/9/2 but was prone to raise off limpers b/c the table was full of them so my first raise would have been standard to him if he was paying attention to me...

No-Limit Hold'em, $0.05 BB (8 handed) - Hold'em Manager Converter Tool from FlopTurnRiver.com

MP1 ($2.76)
MP2 ($7.26)
CO ($11.77)
Button ($2.12)
Hero (SB) ($4.35)
BB ($5.59)
Villain (UTG) ($5.93)
UTG+1 ($5.20)

Preflop: Hero is SB with K, K
Villain calls $0.05, 3 folds, CO calls $0.05, 1 fold, Hero bets $0.23, 1 fold, Villain raises $0.45, 1 fold, Hero raises $1.80, Villain calls $1.55

Flop: ($4.20) 9, Q, 9 (2 players)
Hero ?

So he just called me preflop...I put him on JJ, QQ, AK. Knowing him I am pretty sure that he 5bet shoves with AA and KK so I make that highly unlikely that he holds these but possible.
God how I wish I was in position...
The flop comes Q high.
Can I just check? Or is this stupid? If I bet, I am committed so I have to basically shove anyway if I bet. If he holds JJ, AK he probably folds unless he feels committed with JJ. If he holds QQ, KK, AA he calls and I lose. So does a bet make me any more money?

[daven]

check flop.

[Hoopy]

I think if you just shove he'll fold many worse hands (TT,JJ,AK), by checking you can gain some value from these if he bets them. Also not much can really call your shove apart from QQ,KK,AA and maybe AQ if he plays quite straight forward.