5NL FR QJo in the BB - limped pot

Opp is 40/7 over 16 hands.

On the flop after he calls I have him on A3s,KcJc,KcTc,Kc9c,Q9s+,JcTc,Tc9c,9c8c,KQo,QTo+

The flush card on the turn is bad for my equity as it drops to 40% vs this range, but if I check I think he bets his entire range and I pretty much have to fold. Is it OK to b/f this turn even though I have less than 50% equity?

River does not change my equity much. Is it OK to block bet here? At first I was thinking thin value vs his worse queens because I did not realize on the spot that I was now tying with all his queens (paired board and A kicker on board).

Full Tilt No-Limit Hold'em, $0.05 BB (8 handed) - Full Tilt Converter Tool from FlopTurnRiver.com

saw flop

SB ($2.75)
Hero (BB) ($5.35)
UTG ($5)
UTG+1 ($5.07)
MP1 ($2.85)
MP2 ($2.87)
CO ($5)
Button ($5.34)

Preflop: Hero is BB with Q, J
2 folds, MP1 calls $0.05, 4 folds, Hero checks

Flop: ($0.12) 3, 3, Q (2 players)
Hero bets $0.10, MP1 calls $0.10

Turn: ($0.32) 7 (2 players)
Hero bets $0.20, MP1 calls $0.20

River: ($0.72) A (2 players)
Hero bets $0.30, MP1 calls $0.30