I would normally check this flop 3way and versus BB who has range advantage but this time decided to bet it as opponents seemed call happy.
-As played, facing the check jam, do we have to sigh call it off?
-Leveled myself into thinking there was enough combo draws, pair+draw, flush draws and maybe 7x in his range to call it off.

PokerStars - 2000/4000 Ante 600 NL - Holdem - 9 players
Hand converted by PokerTracker 4

SB: 80,589 (VPIP: 9.33, PFR: 5.41, 3Bet Preflop: 3.23, Hands: 75)
BB: 274,667 (VPIP: 100.00, PFR: 100.00, 3Bet Preflop: -, Hands: 1)
UTG: 104,491 (VPIP: 14.29, PFR: 14.29, 3Bet Preflop: 14.29, Hands: 14)
UTG+1: 298,441 (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 12)
MP: 269,323 (VPIP: 14.29, PFR: 7.14, 3Bet Preflop: 0.00, Hands: 14)
MP+1: 101,485 (VPIP: 42.86, PFR: 35.71, 3Bet Preflop: 20.00, Hands: 14)
MP+2: 148,730 (VPIP: 38.46, PFR: 25.00, 3Bet Preflop: 0.00, Hands: 14)
Hero (CO): 99,101
BTN: 888,321 (VPIP: 12.90, PFR: 6.45, 3Bet Preflop: 6.67, Hands: 31)

9 players post ante of 600, SB posts SB 2,000, BB posts BB 4,000

Pre Flop: (pot: 11,400) Hero has Q Q

fold, fold, fold, fold, fold, Hero raises to 8,000, BTN calls 8,000, fold, BB calls 4,000

Flop: (31,400, 3 players) 7 4 6
BB checks, Hero bets 18,452, fold, BB raises to 266,067 and is all-in, Hero calls 72,049 and is all-in

Turn: (212,402, 2 players) 5

River: (212,402, 2 players) T

Fine spot to check back some % of time. If you have a read they call light I like cbetting
My concern is with the sizing. You have the chance to manage the pot at pleasure, but your CB sizing is a recipe for disaster if you face a raise
Cbet 30% next time IMO

Check flop is interesting for balance but cbet should be the main move and I think the sizing is good on this texture 3way. Snap call the shove 100% of the time, he has tons of FD/overpairs.