What is villains stats? I like the 3bet pre if the opponent plays straightforward and doesn´t bluffraise or float or try to be tricky in some way. Otherwise I think you should just flat pre with those non-premium aces.
Villain probably puts you on aces when you 3bet so he can play perfectly against you. His range when he calls the flop is hard to say without stats but against a REG I put him on a range of: flushdraw, OP, maybe 2P but he would raise the flop somtimes with it probably, TP, wrap, combodraw but he would raise the flop with these often too, pair+ draw, 2pair +draw would he also problaby raise the flop with. If you double barrel his range to continue I think are T8, TP+flushdraw maybe wrap, 67, good 2P he didn´t raise the flop with, combodraws and I think he will fold TP, probably wraps, bad 2pairs. So he could continue with a lot of hands and 67 got there so I think the best play is just to check and hope to see a showdown cheaply and a brick river. The bad thing about checking is that you have to fold if he bets, and you could get som value from draws, TP+draw type of hands and you have 5-6 outs and if the board pairs you often have the best 2-pair.
But if you double barrel and he calls, you´re in a tough spot on the river. If a brick comes you could triple barrel to fold out all of his draws, bad 2pair hands and that lot´s of hands you could fold out. But it´s a risky play and maybe a little bit too spewy with a lot of variance. If you check on a brick if he´s good he could bet out with missed draws and you have to fold. If the river hit´s the flushdraw you have to check-fold.
If villain is a loose-passive player they could also sometimes call the flop with sets, 2np pair, 3np + gutshot and things like that. But they also call much lighter so they would call a double barrel with a much broader range like OESDs maybe, so I wouldn´t barrel against them.