Here was my range and thought process before my decision:
AT makes sense pre. The flop call and turn shove are incongruous. If he has such a strong hand, why go huge on the turn? I'm drawing to 3 outs if my kicker is an overcard. Does he think I will pay him off with AJ+? If yes, why go huge here? I've already barreled twice, there's a good chance I will again on the river. If I check river, he can still bet after me. AT is possible but I discount it.
A2 makes sense pre. Shoving does prevent his hand from being counterfeited if the board pairs. Also, every card in the deck is an overcard, so if Hero shoves river he is in a tight spot. A2 is a more likely hand than AT.
AA/TT are likely 3b from this player and usually would have waited another street to extract more value. I don't think these hands are likely.
22 makes sense pre but like the sets above, would likely have waited for another street to extract value. Slightly more likely than AA/TT, but not likely.
Broadways KQ/KJ/QJ would not be this aggressive drawing to 4 outs. Close to 0% he turns up with these.
AQ/AJ would be a weird shove and not what I expect from this player. Too much SDV to turn these hands into bluffs and they aren't strong enough to be value bets. Possible, but I discount them heavily.
33,55-99, JJ/QQ these would be bluffing hands that he knows are no good. If I have TPBK I can fold to a shove. But if he gets called he is basically screwed. 33 and 55 have a few extra outs with a straight draw, but not much.
What is right/wrong with my thinking here?