[AviD]

I don't think a TAG is going to call your river lead with 66 or less, he may bluff at it but chances are he'll fold. He may call a lead with a hand like JJ-88, but not bet them. Beyond that, you are ahead of AJ-A8, which he'll probably bet and you can CR, but you have an A so that decreases the chances he does. Plus if you bet (assumed value bet on his part) and he has an A, he may very well raise figuring you were betting a Q or the like. So you get your 2BBs in.

Ultimately I like betting here and calling a raise. I wouldn't want to a miss a value bet from a hand that would have called, nor do I want to face a 3-bet from a TAG (creative, tricky, occassional suboptimal playing style) on the river who may have something like A7. I don't think he'd check thru the turn with AQ, certainly not AK unless or some strong hand (set+) unless he is pretty tricky. You may get a mid A to raise the river, and you'll likely get called by 88-JJ. You probably won't get called by 66-33 so betting out and checking through have the same net, except you have the info about his hand which you really don't need, I'd rather collect the bet from middle pockets or induce a raise from a weaker A.