I think you can double barrel here. You have picked up some equity on the turn as well as this is a good place where you can effectively represent a 2 or a big Q here with a decent show of strength. A lot of times you are going to get floated here because the BB isn't going to believe that you had much of anything and that your flop bet was purely a c-bet taking a stab so I think that the double barrel here is an effective bluff. What I would caution here though is pay careful attention to what he does, as if you get raised or played back at you have to fold. I don't think that he can really flat the 2 barrel here, that he will have to raise/fold to the pressure (I also don't think that a Q holds up well to the 2 barrel here either unless maybe AQ). I would go ahead and fire again and see what happens.

Hmmm… the Ace is a really interesting card, because that should solidly hit our range and should look like a 2 pair hand to him now (AQ being something solidly in our represented range). The thing that is concerning at first glance here because he is a 7/4 so the Ace should collide very strongly with his perceived range, but I don't believe it does with his flatting range from the BB. My guess is that if you put in the 3rd barrel you should get him to fold. As far as what I think he has here, could be 77-JJ,  AQs (maybe), AJ. I don't think this is AA, KK or AK as I believe he would 3bet you with that and confidently. This could be a marginal Ace for him (AQ, AJ) or more likely it could be a smaller pocket pair that doesn't believe you from the button. I think the A is a very favorable card for you to push him off whatever he has and take the pot down.