QQ overpair babydeep

villain is 20-15-4 with 50% fold to cbet over 250 hands. His big pots so far have not involved showdowns. He barrels happily
his range is broad here preflop ip and multiway and it's hard to see that flop narrows i too much

what's my turn plan?

$0.10/$0.25 Ante $0.05 No Limit Holdem
9 Players
Hand Conversion Powered by weaktight.com

Stacks:
Hero ($53.50)
UTG+1 ($9.64)
MP1 ($79.84)
MP2 ($64.17)
MP3 ($60.36)
CO ($77.20)
BTN ($28.27)
SB ($63.51)
BB ($50.80)

Pre-Flop: ($0.80, 9 players) Hero is UTG
Hero raises to $1, 2 folds, MP2 calls $1, 1 fold, CO calls $1, 2 folds, BB calls $0.75

Flop: ($4.55, 4 players)
BB checks, Hero bets $3.50, 1 fold, CO calls $3.50, BB folds

Turn: ($11.55, 2 players)

b/f

+

pray for river J (lol at full nit)

Villain raises {TT-99,T9s} on the flop I think. There are two combinations of QJs and three combinations of 88 that beat you here. Also, 76s may have called with a gutshot, especially 7h6h. However, most of villain's range here is still flush draws or a top-pair kind of hand. We have >50% equity here and villain may call a $9ish bet with his flush draw. Does villain raise a lot on the turn/postflop? I'm looking to value bet here and check/call a safe river.