No reads. How do we play this?

Full Tilt Poker
No Limit Holdem Tournament
Blinds: t25/t50
7 players
Converter

Stack sizes:
Hero: t1445
UTG+1: t2290
MP1: t935
CO: t1135
Button: t1615
SB: t4620
BB: t1460

Pre-flop: (7 players) Hero is UTG with Q A
Hero raises to t150, 5 folds, BB calls t100 (pot was t225).

Flop: A K 3 (t325, 2 players)
BB checks, Hero bets t200, BB calls t200 (pot was t525).

Turn: Q (t725, 2 players)
BB checks, Hero..?

Preflop and flop are fine.

Turn is just an ugly decision. I probably go broke if he has the flush.

Bet 550 and call shove imo/

I don't see the advantage in betting the turn. check behind and re-evaluate river (bet if checked to, call a reasonable bet, fold to four spades).

Why give him a free card? Definitely put in a bet and call a shove here. Yeah he has a flush sometimes, but not often enough for this to be -EV.

Not betting the turn is horrible.

Why is it "horrible"? Two reasonable draws just hit, both the straight and flush. What hand does he call on this turn with that we're beating? And when he shoves we are never ahead (only maybe to A3 or AxJs). If we want to extract more value from weaker aces then we can do so on the river. The only disastrous situation is when a fourth spade hits and he bets it, but that's rare.

If you check the turn and he leads out for, say, 500 or 600, are you folding? If you're not prepared to fold your AQ to a bet, and you're WA/WB here, there is no added value to leading the turn. Might as well try to keep the pot small and get to showdown as cheaply as possible. In this situation a free card looks virtually harmless.