Fairly common difficult spot. Assume that villains are solid TAGs, and let's also assume that AA/KK are very unlikely. My standard preflop play with AQs is to call UTG raise OTB, but let's think about postflop here.

If we cbet 3/4 pot ($300) and are called by one player, then pot size is $1010 and we have $565 behind.

We could c/f all streets, but that seems weak and we aren't protecting our hand.

Seat 3: UTG ($1025.40 in chips)
Seat 4: CUTOFF ($1,261.00 in chips)
Seat 8: HERO [ QD,AD ] ($1,000.00 in chips)
Seat 9: SB ($1,019.35 in chips)
Seat 10: BB ($600.30 in chips)
ANTES/BLINDS
SB posts blind ($5), BB posts blind ($10).

PRE-FLOP
UTG bets $35, CUTOFF folds, HERO bets $135, SB calls $130, BB folds, UTG calls $100.

FLOP [board cards 4C,QC,7D ] (pot $410)
SB checks, UTG checks, HERO...