$2NL KK vs lots of PF action, Q-high flop

-edit sorry, wrong stakes in title, this is $5NL-
Villain was running 36/18/20 vpip/pfr/3-bet over 11 hands, so not a great sample.

When he 3-bets, I'm putting him on something like TT+, AJs+, AQo+ (is this reasonable? I haven't done much of this)

When he just calls my 4-bet, I'm thinking it can only be QQ+, maybe AKs or JJ, weighted towards QQ, since KK is unlikely and AA would probably shove.

What's my action on the flop? Since I put him on a range that crushes me, do I just sigh and c/f?

No-Limit Hold'em, $0.05 BB (7 handed) - Hold'em Manager Converter Tool from FlopTurnRiver.com

MP2 ($5)
Hero (CO) ($4.80)
Button ($16.05)
SB ($5)
BB ($2)
UTG ($5.74)
MP1 ($7.86)

Preflop: Hero is CO with K, K
3 folds, Hero bets $0.15, Button raises to $0.65, 2 folds, Hero raises to $2.15, Button calls $1.50

Flop: ($4.37) 9, 4, Q (2 players)
Hero ???