KK 3bet pot, weird turn card

Villain is 18/11. We've been in a lot of pots together and I've been 3betting him a ton. I've had the goods every time and it was just a card rush. He folded each time and this is the first time he's flatted. I expect a lot of PPs here, some AQ, some SCs, and not a lot of AK.

Should we be betting this turn? Betting here is folding out all his other pocket pairs and looks extremely strong, and we're getting owned by JJ/QQ now. Should i just check and bet a safe river? I'd take this line with air, but for value I don't see how we'd get called by a worse hand since we're showing so much strength

Full Tilt Pot-Limit Hold'em, $0.50 BB (9 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

saw flop

MP2 ($46.95)
MP3 ($22.35)
CO ($50)
Button ($34.25)
Hero (SB) ($51)
BB ($36.55)
UTG ($50)
UTG+1 ($64.55)
MP1 ($48.75)

Preflop: Hero is SB with Khttp://www.flopturnriver.com/pokerfo...lies/heart.gif, Khttp://www.flopturnriver.com/pokerfo...es/diamond.gif
5 folds, CO bets $1.50, 1 fold, Hero raises to $5, 1 fold, CO calls $3.50

Flop: ($10.50) 3http://www.flopturnriver.com/pokerfo...lies/heart.gif, Jhttp://www.flopturnriver.com/pokerfo...es/diamond.gif, 3http://www.flopturnriver.com/pokerfo...es/diamond.gif (2 players)
Hero bets $6, CO calls $6

Turn: ($22.50) Qhttp://www.flopturnriver.com/pokerfo...ilies/club.gif (2 players)
Hero bets $12, 1 fold

Total pot: $22.50 | Rake: $1.10

hes going to check back this turn way more often than he will bet

fire away and give him the opportunity to call you down with Jx and worse pairs.

seems well played to me.
especially given history he's gonna be suspicious - let him call with the ok part of his range AQ, his AJ, his AK, his TT, etc. Plus there's some element of flush draw that's calling turn but not river... With his made hands he wants to see a showdown, and is calling way more often than betting when checked to with the weak junk in his range - betting this turn looks like AK/QQ+ so go for it and let him soul=read poorly.

It's just a crappy turn card to get value and a good one to bluff I still think a bet is best