kk, set on monotone board facing heat

[daven]

OK, simple answer is shove flop - but I want to think a little. I've had top set on a monotone flop three times the last two days and got it in on the flop each time = leak? (-4.5buy-ins on those hands, so want to think about it a little)
Villain is a little loose pre, but pretty solid post-flop - folds a LOT to c-bets, doesn't seem to semi-bluff.
I've repped strength pre, most likely looks like AK/QQ+
Flop. I can either call the re-raise or push. I doubt that opp is doing this with a flush draw, and he knows that my weakest likely holding is QQ, more likely TPTK, king set or AA. Situation is that i'm, most likely up against another set or a made flush. Against a flush I got 7 outs - is it worth flat calling here and re-assessing, or should i simply push?
Full Tilt No-Limit Hold'em, $0.50 BB (9 handed) Full-Tilt Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

BB ($50.50)
UTG ($134.75)
UTG+1 ($68.50)
MP1 ($63.15)
MP2 ($34.15)
MP3 ($50.75)
CO ($44.90)
Button ($57.80)
Hero ($95.50)

Preflop: Hero is SB with K, K.
5 folds, CO raises to $1.5, Button calls $1.50, Hero raises to $3.75, 1 fold, CO calls $2, Button calls $2.

Flop: ($11.25) 3, K, Q (3 players)
Hero bets $7, CO folds, Button raises to $14, Hero raises to ? or calls?

[dev]

If you flat it the only way you get away is if another heart falls. Most likely your AI by the river anyway. I don't think Button is deep enough for you to get away from this hand.

Also, you have 7 outs for the turn to hit you with a boat or quads, but you have 10 on the river. It's about 1% worse than a flush draw and about 2% better than an OESD.

On the chance that he himself has AhAx or AhKc or QQ or KQ, I think we're pretty much going for broke here.

If you can put him squarely and only on a flush then we can call and fold to a decent turn bet, otherwise we have to get it AI here at some point.