50NL: QQ river shovified

Villain is 5/4 with 4% 3bet over a small sample of 75, during that time he has not shown down anything worth noting or gotten out of hand in some way. He should be fairly straightforward. I'm a bit confused as to what kind of range checks this turn to shovel the river. Thoughts?

Full Tilt No-Limit Hold'em, $0.50 BB (7 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

MP1 ($61.50)
Hero (MP2) ($62.80)
CO ($81.55)
Button ($50)
SB ($37.45)
BB ($52.80)
UTG ($19.15)

Preflop: Hero is MP2 with Qhttp://www.flopturnriver.com/pokerfo...lies/heart.gif, Qhttp://www.flopturnriver.com/pokerfo...ilies/club.gif
1 fold, MP1 bets $1.50, Hero raises to $4.50, CO calls $4.50, 3 folds, MP1 calls $3

Flop: ($14.25) 2http://www.flopturnriver.com/pokerfo...ilies/club.gif, 9http://www.flopturnriver.com/pokerfo...lies/heart.gif, 6http://www.flopturnriver.com/pokerfo...lies/heart.gif (3 players)
MP1 checks, Hero bets $8, CO calls $8, 1 fold

Turn: ($30.25) Khttp://www.flopturnriver.com/pokerfo...es/diamond.gif (2 players)
Hero checks, CO checks

River: ($30.25) 2http://www.flopturnriver.com/pokerfo...lies/spade.gif (2 players)
Hero bets $11, CO raises to $69.05 (All-In), Hero folds

Total pot: $52.25 | Rake: $2.60

I would c-bet flop harder for sure multiway at least 2/3 to 3/4 pot.

As played the turn is a card I would be double barreling almost always as it improves your range more than it does villains. If he raises its an easy fold. If he calls c/f'ing river is prob best.

The problem is if you check the turn you need to be checking with your monsters which is bad given the board unless villain is a floater, but without reads that he is capable of doing this plus the fact @ 50nl people don't float people who 3Bet early position openers betting seems best. Also if you don't bet you are giving him an opportunity to bluff 2 streets with a flush draw when it is likely you do not have a king and infinite odds to draw to his flush should he check behind.

As played I don't understand the river bet as possibly the only hands he could call with that you are beating are 1010 & JJ. If you check the turn you have to check river as well since bet/folding for value seems really thin.

I think it's all fine. There's not much that you can get value from on that flop anyway, unless MP1 is dumb. I don't think you can get value from JJ, TT from a 6/5 on that turn, if that's even in his range.

I c/f river. I don't hate the blockbet.