typical situation, that ive still never managed to figure out

[RunDownHouse]

I'd expect a TAG to c/r this flop with Js a fair amount of time, so that holding can be discounted some. Given that, I really think you should bet the turn here. Nut flush draw, better chance of splitting with another A, all that good stuff that's been mentioned.

The river is tougher. If he has a read on you, he has to think that you'd value bet almost any pair on the turn, and would only check behind some A-high hands and draws. And if he's good, he's not going to bet if he expects you to fold near 100% of the time, as you would with any draw. So this might be an A hoping to fold a weakly-played better A, but more often I think he's betting a hand better than A-high (or at least most A-high), since he wouldn't make a bet with no value. He should know you're intent on either folding the river UI or trying to get to showdown with a not-so-great hand, which in this case would not include most pairs.

Its late, did that make any sense?