qq turn top set, bet sizing question

Cake Poker No-Limit Hold'em, $0.04 BB (8 handed) - Cake-Poker Converter Tool from FlopTurnRiver.com

Button ($4.69)
SB ($3.66)
Hero (BB) ($6.93)
UTG ($4.52)
UTG+1 ($1.70)
MP1 ($10.59)
MP2 ($3.83)
CO ($4.45)

Preflop: Hero is BB with Qhttp://www.flopturnriver.com/pokerfo...lies/heart.gif, Qhttp://www.flopturnriver.com/pokerfo...es/diamond.gif
4 folds, CO bets $0.11, 2 folds, Hero calls $0.07

Flop: ($0.24) 10http://www.flopturnriver.com/pokerfo...ilies/club.gif, 5http://www.flopturnriver.com/pokerfo...ilies/club.gif, 8http://www.flopturnriver.com/pokerfo...lies/spade.gif (2 players)
Hero checks, CO bets $0.16, Hero calls $0.16

Turn: ($0.56) Qhttp://www.flopturnriver.com/pokerfo...ilies/club.gif (2 players)
Hero bets $0.38, 1 fold

Total pot: $0.56 | Rake: $0.03


opp is new at the table, i dont have notes. so here i am, out of position with a strong hand, assuming opp doesnt have the flush. reason for not 3betting pre is a somewhat cautious preflop table dynamic, and I was fairly confident opp would have just folded here. hence, pre flat call, flop comes undercards, great. i check to him, letting him cbet into the pot, i flat. turn puts a flush out there, but also gives me top set, and so im left with the question of how to maximize profit

any thoughts on what line i could have taken to get more out of this hand?

I hate your OOP flat PF. If you don't 3bet QQ vs a LP raiser what are you ever going to 3bet?

3 bet preflop for sure. "Villain is unknown" and "I was pretty confident he was just going to fold" are pretty inconsistent. You'll get called by tons of worse hands here usually, and if he folds so what, playing QQ oop without initiative is giving up more value than 3 betting and folding out the weaker end of his opening range is. 3-bet and bet bet jam whenever you flop an overpair = printing money.

As played c/r this flop for value and again expect to be called by/get it in against a lot of worse hands.

thanks for the feedback, i probably dont 3bet quite as much as i should.

looking back, the way i played this hand seems kinda silly.