Standard laydown or outplayed?

[4thstreetpete]

Party 30/60

Villain is your average 2+2 multitabling TAG. 15.4/11/2.94 after about 6K hands.

I have A [img]/images/graemlins/diamond.gif[/img]A [img]/images/graemlins/heart.gif[/img] on bb.
villain in CO raises, sb calls raise, I 3 bet.
villain calls sb calls

flop is T [img]/images/graemlins/spade.gif[/img]K [img]/images/graemlins/diamond.gif[/img]2 [img]/images/graemlins/club.gif[/img]

checks, I bet, CO calls sb folds

Turn K [img]/images/graemlins/heart.gif[/img]

I bet, CO thinks about it and calls

River 5 [img]/images/graemlins/diamond.gif[/img]

I bet (?), CO thinks and raise
I fold

I'm thinking this over of how badly I played this hand. Is check/call the river the best play in a situation like this or value bet the river?

Probably my biggest leak is not being able to lay down a hand on the river. I'm thinking back of all the times that I find myself in this position and almost always lose in a situation like this. Would a very tight but aggressive player in CO be willing to make a play at me on the river knowing that I 3 raise the flop and bet all the way? Nice size pot.