I could see villain checkraising for value here. Your range should be a ton of Ax and flushes and if you're betting all of that on the river he can maximize his value with the strongest part of his range. Whether or not your size influenced his river play is a guessing game.

I like the idea of your thin bet but I'm on the fence about if I like it or not. Since the flush came in it's 1) really hard for you to be bluffing so why would he call light and 2) everyone's afraid of flushes you so might not get called as light. I don't know how often players will donk into 2 players on the flop, lead again on the turn and then x/c 8x on this runout.

When he raises I'd fold. While it's an odd spot, this should be among the worst hands you're going for value with so folding it should be ok. If you split your range by betting larger with better hands and tiny with only thin stuff then that might be a problem so throw a few strong hands into your range when you do this.

I'd have to say it's a fold, since you beat A3, A4. I don't think they raise for value.
Flush comes in too. I'm not sure what calls a 3rd barrel here anyway so I might just check back, but that might seem nitty.
Though vs an unknown I opt toward the folds. He can play 88 this way too I think.
I just don't think we can make a profitable call unless we have specific reads on opponent.

I'm folding the river. It feels grim when we try to make a thin value bet and get raised but it's unlikely he's ever doing this with a worse value hand.

He's probably assuming that just about any hand which calls a third barrel will bet if he checks anyway, so a check raise is the best way for him to maximise his value. Maybe I'm giving him too much credit but I still can't see how we're ever good here enough to hero call.

I'm trying not to be results orientated but I don't think I would bet the river myself. Many 10NL players will lose their nerve with medium Ax once the flush card hit and only go for two streets intending to call if you bet. His checking range will still be quite strong here for the average micro stakes player

I think the fold is the right play. I'm not sure I like the river bet to be honest. I think the idea is good but I'd want him to be able to call some weaker hands and there are not many I can see. I think the sizing is good if you do do it, and your hoping he has like TT, which can't believe you maybe? I'd just check it back though and make him steam when he sees you flip trips and he missed out on value from the draw he was chasing.

Pretty reasonable hand overall. Thin value on the river is actually super thin, I doubt we are making that much. Anyway, fine, and obviously fold to the raise.