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 Q, Q
4 folds, CO bets $0.11, 2 folds, Hero calls $0.07

Flop: ($0.24) 10, 5, 8 (2 players)
Hero checks, CO bets $0.16, Hero calls $0.16

Turn: ($0.56) Q (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?