9 handed table, effective stacks are $50. BB is a 35/5/3 player.

I raise UTG w/AQ, folds to BB who calls.

flop is J33 w/2 spades.
check, I bet $3, he calls

turn is an offsuit 4
check, should I double barrel here? It seems like he has a small pair or a Jack the majority of the time and a draw the rest. I only ask cuz Renton said that in a RR pot if you bet this flop you should always be prepared to double barrel. Is this true in raised pots as well?