Top 2 pair on paired board on the river

Pre call is standard.
OTF I think you can check raise, that should be fine.
OTT cbet is ok.
OTR I don't think villain would call with very many weaker hands if you barrel again, so checking is fine. I would go with check call probably because your play looks like a missed draw and I can see villain bluffing a lot. Imo he shouldn't have very many stronger hands because those would have likely stacked off OTF or OTT.

I checked this with Snowie too and it thinks you played it perfectly. OTR it would check call but it has only a very very small EV difference. Villain can have some K7,J7,87.

I called, he shows AA. Can you look at his play? Is it standard?
Is it good to cbet that small on that flop?
If I had missed draw (what I thought it looked like) why would he bet so much OTR?

No I don't think villains play is standard.
When you xr the flop you have some bluffs and some 2pair+ hands. That turn card is actually very bad since it completes T9 and opens another flush draw -> half of the deck is bad for villain OTR. Snowie would actually recommend to fold AA OTT vs your bet and I believe that would be a good move.

OTR Snowie would just give up. Villain might think shoving is ok since draws miss and now he can rep some full houses too -> he thinks he has good fold equity. But imo he shouldn't turn his hand into a bluff.