5-10 pl, qq hand against big and small stack

[Nero]

5/10 plhe, 5 handed
Stacks: me ~1800, sb ~2250, bb ~450

I open UTG for 35 with red QQ. called by sb and bb.

flop(105): 10 7 3, two spades. checked to me, i bet pot, both call.

info:
bb - call could be overcards or draw. he would he bet/raised a pair or set into a two-toned board.

sb - call is a 100% draw, either oesd or flush.

turn(315): offsuit 6. check, check, I...........and how much?

[turnipmonster]

my initial reaction is bet 300, you cannot give a free card here. the bb is looking quite pot committed, so it's really the sb you have to focus on. if you check, you would be checking for pot control reasons and you would have to be prepared to call a pot bet on the river. you would also be giving a free card to two drawing hands, which really sucks. I don't think you can check here if your reads are correct.

if you bet and are raised, I think you have to lay it down particularly if the bb calls unless he's just a complete moron.