NL50, KK on monotone action flop. is this always push?

[Anycall]

villain here is running 27/7 over 120 hands. when i made the cbet on flop, i actually liked my hand. but after i was check raised on this flop, i figure he has to have at least 2P to make the check raise on this action flop. what would be the best way to proceed with this hand. as you can see, i pushed the flop. looking at the stack sizes though, i think i have almost no F/E. any other way to play this hand? thx.


Full Tilt Poker - No Limit Hold'em Cash Game - $0.25/$0.50 Blinds - 6 Players - (LegoPoker HH Converter)

SB: $97.80
BB: $45.05
<font color="black">Hero (UTG): $137.35</font>
MP: $98.25
CO: $55.05
BTN: $76.75

<font color="black">Preflop:</font> Hero is dealt K[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/spade.gif[/img] (6 Players)
<font color="red">Hero raises to $1.75</font>, MP folds, CO calls $1.75, 2 folds, BB calls $1.25

<font color="black">Flop:</font> ($5.50) 9[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img] Q[img]/images/graemlins/spade.gif[/img] (3 Players)
BB checks, <font color="red">Hero bets $4.50</font>, CO folds, <font color="red">BB raises to $19</font>, <font color="red">Hero raises all-in to $135.60</font>, BB calls all-in for $24.30
Uncalled bet of $92.30 returned to Hero

<font color="black">Turn:</font> ($92.10) 9[img]/images/graemlins/diamond.gif[/img] (2 Players - 2 All-In)

<font color="black">River:</font> ($92.10) 6[img]/images/graemlins/club.gif[/img] (2 Players - 2 All-In)