Villain calling 40% of my buttons, 3betting ~ 20% and opening ~ 60% of his buttons. I cant remember situation how he is adapting on paired flops. How u play that hand?

PokerStars - $6.67+$0.33|30/60 NL (2 max) - Holdem - 2 players
Hand converted by PokerTracker 3

Hero (SB): 2,025.00
BB: 975.00

Hero posts SB 30.00, BB posts BB 60.00

Pre Flop: (90.00) Hero has Q 6

Hero raises to 120.00, BB calls 60.00

Flop: (240.00, 2 players) Q 5 5
BB checks, Hero bets 120.00, BB calls 120.00

Turn: (480.00, 2 players) 3
BB checks, Hero ???

given his frequencies i think we can discount 5x from his range.
I don't see a lot of hands we get value from on the turn besides single spade floats which will fold to a river bet. and if we check i expect him bluff lead river with thoose hands so we don't lose value from them.

I believe e 1/2 bet should be ok here...if he doesn't check-raise often then it's ok to bet.A check back it's also good giving you a free river card that may improve your hand but given the flushy board I think you should charge the villan rather that giving him a free card.He could call your turn bet with many hands like:some high cards,one to flush,a better queen,66-JJ(given he didn't 3-bet preflop it's not likely he has a pocket pair) he can slow play a flush though.If he plays back beware.Call if he raises 2xYour bet but fold if he goes deeper.On the river look for a cheap showdown and if the 4th to flush comes,fold to any bet...I hope I helped...
note:this is how I act and my strategy so do not take for granted everything I say,I might be wrong also!