$2 NLHE Full Ring: QQ in position 3-way flop, one overcard

PokerStars - $0.02 NL - Holdem - 7 players
Hand converted by PokerTracker 4

Hero (CO): 107.5 BB
BTN: 81.5 BB (VPIP: 16.67, PFR: 0.00, 3Bet Preflop: 0.00, hands: 8)
SB: 57 BB (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 10)
BB: 120.5 BB (VPIP: 66.67, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 3)
UTG: 100 BB (VPIP: 14.75, PFR: 6.56, 3Bet Preflop: 10.53, Hands: 63)
UTG+1: 100 BB (VPIP: 20.00, PFR: 10.64, 3Bet Preflop: 7.41, Hands: 239)
MP: 87 BB (VPIP: 40.00, PFR: 40.00, 3Bet Preflop: -, Hands: 10)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has Q:diamond: Q:spade:

fold, fold, MP raises to 2 BB, Hero raises to 6 BB, BTN calls 6 BB, SB calls 5.5 BB, fold, fold

Flop: (21 BB, 3 players) T:diamond: K:club: 4:diamond:
SB checks, Hero checks, BTN bets 1 BB, SB calls 1 BB, Hero calls 1 BB

Turn: (24 BB, 3 players) 4:spade:
SB checks, Hero bets 14 BB, fold, fold

Hero wins 23 BB

Really just had no clue what to do here, larger 3bet I think would've helped? Ended easily for me but I played badly and it could have gone very differently.

If he folds there prolly checking turn and try and induce river bluff wouldve been the answer.

Pretty hard to fold out better on the turn, and worse probably isn't calling, so I agree that check/call is probably the right line.

Btn and SB are fishes because they can just do that with monsters, don't know why you check that flop, and then just call a 1bb bet if you would donk bet river? Just bet 2/3 flop, 1/2 turn, 1/2 river

I think you are ok checking and seeing the weak bet on the flop and then call.
The turn bet was pretty big representing AK, don't know if you pushed off a K little, probably not.