Villain has 62k post flop, and is likely to be doing this with sets and two pair in the late game
Doing what? He's called an A84cc flop 32big blinds deep in a single raised pot, and again on a flush completing turn card. In my experience that's a small flush way more than it's a set or 2p, remember he'd have 3bet AA preflop most of the time, and we have an ACE (so only 1 combo) he'd raise the flop with 88 at least sme of the time, plus there is only 1 combo, same with 44, 84 would be the worst turn call ever unless he had a flush with it - he prolly won't bet 84 anyways, if you're beat OTR it's prolly to a hand with 84 and flush

something like that, or a A84* hand that didn't raise the flop (I guess if it was A842 or something he'd just call the flop)
v unlikely to be doing this with worse flushes.
Still he hasn't done anything up to this point except take a passive line with what we can assume OTR is a weak hand, given the passive flop line and the fact we can block out 1/3 of the boat combo's I'd go as far as to say that he'll show you a J or T high flush here about 80% of the time, there are loads of combo's of hands he'll peel a flop bet with that have weak(ish) clubs in it,

pair/gutshot/fd he'd just call with that hand almost always,

something like that loads of combo's and given we have the NFD and an ACE there is an ACE on the board it's safe to assume he'd call with these hands over raising near on always.
As played though, it's a pretty easy chk/fold. He won't (or at least defo shouldn't) bet worse flushes or naked

for value, he prolly wont turn a naked 8 or A4** into a bluff (although it's a good(ish) spot given how you're folding the majority of the time you're checking this river) so most of the time will chk/chk and you win but when he ships he just has a boat. Jamming has a little merit but I think on the bubble he'll fold most of his flushes so it's really just isolating yourself vs his boats when you ship the river.