Ran into this spot in a small tournament ($10) on Bovada, new to the table so pretty much no reads on anyone. We had just won the last hand in a checked down pot from the SB after betting the river (probably irrelevant though).

Blinds: 75/150

UTG [5,020]
UTG+1 [5,225]
MP1 [5,000]
MP2 [6,610]
HJ [4,700]
CO [8,300]: HERO
BTN [8,120]
SB [4,855]
BB [4,550]

Preflop: Hero dealt AdJh

5 folds, Hero raises to 400, BTN calls, SB calls, BB calls...

Flop (1,600): 6s10hJc
Sb checks, BB bets 300, Hero raises to 900, BTN folds, SB folds, BB calls...

Turn (3400): Ac
BB bets 1,050, Hero raises to 4,000, BB folds...

Feel pretty good that we have the best hand here, maybe he shows up with 66 sometimes but never really concerned me. Thought he might have like J10 or something like that. Pretty surprised he folded given he had already put in over half his stack and was getting pretty good odds to call.

My question to you is, how can I improve my sizing to maximum value OTF or OTT? Can we flat the turn and hope the river bricks? Can we ever flat the turn and fold the river on a terrible card (Qc)? Or am I overthinking this and just GII on the turn every time and if he folds we still pick up a nice pot?

Thanks everyone.