The villain suffers from the fancy play syndrome and has a huge ego. Limped with AA, checked back, I bet my two pair, he shoved. One time he check-minraised, I flatted with my flush draw, he lead out with a shove on the turn (blank).
Here I was a little bit concerned with his passive line. At this point my river value bet seems bad, because any pairs he could hold are likely to have been played faster. That said, now I don't think we're losing a ton of value by checking behind here. I also expect his missed flush draw to try and prevent the showdown. So, is it a good idea to check back and see if he is capable of calling 2 streets with a draw or whatever? Also, is it a fold after he check-shoves?

this villain is just bad, spazzy, and impatient it looks like. Against this guy, call that shove and smile. U r waaay ahead of his range.

Yeah, I'm not too worried about calling his shove although Mr Smarty Pants happened to have it this time. Or... well... I really don't know. I'm doing really, really well until I make a funky hero call, and... float with 55% ITM at these stakes... That's why I'm asking, I want to bust that leak so badly... Do you guys have any other opinions about calling a shove?
But the ultimate question is about checking behind for info. I mean, OK, if we induce a 'high class' shove with air -- good. But. I'm 100% sure he's playing all his made hands that we beat much more aggressively, with a lot of paroxysms attached. So, obviously, we're not getting more value if his draw missed. And when he check-raises, busted flush draw happens to be the only hand we beat. On the other hand, when we check back, we can understand his calling range better. No?

checking back river is super results oriented.
also if you even consider checking back river for information you have far too little understanding of your opponent's game to fold to his check/shove.

OK. This basically boils down to the assumption that he bluffs about 33% of the time here. Let's forget that he's 'fancy' and consider him as a vanilla longball LAG. Is it a safe assumption in this case?

I think we never check back here. We bet/call vs most If not every villain and just puke/facepalm when he happens to have T8 or KT... I'd expect him to only have KT or T8 of hearts here played this way which means those two hands plus the 3 combos of QQ makes 5 total hands all that beat our holding.

I'd also expect QQ to raise a decent percentage of the time to protect vs our (mostly) draw heavy BTN open/double barrel range here, leaving even less hands that he shows up here that beat us.

Your line is fine IMO vs such a ridiculous villain. Just unfortunate he had the very narrow range of hands that beats us.

no, if you think that all you beat is bluffs then you should fold.