I will not give myself the check
I do not like his play. He took down the pot but put too much at risk to do so in my opinion.
Since hero bet 6x pre doubt he has an 8 or 3. Even AJ suited would be the low end of his range. Most likely this flop missed the hero. I (villain) can rep a pretty big range with call call pre flop.
Why only bet 1/4 of the pot. Any strong Ace or pair will call. Bet 1/2 to full pot and to fold out the villain if he blanked. If he calls you can put him on JJ+.
If villain under bet the flop then under bet the turn is consistent. That 5 should not have hit the hero. Maybe hero picked up a flush draw.
I missed the only way to take down the pot so time to bluff. I don't think hero has an 8.
Villain put way to much as risk to take down $450. Hero could be on an 8 and will get a call for sure. AJ could call. Villain could have bet 2x the pot for basically the same fold equity.
If going to raise then need to make it 6x with 4 in the pot. Need to raise some weaker hands here to balance your range. I would much rather he raise with 98s 87s that have more chance of making a disguised premium hand. I think a check would have been better here.
Check top pair on a dry board to hopefully get max value is standard. I am curious as to the small bet. Villain could be on a bigger J trying to get value but still a clear call. Seems like KQ QT would have bet more to try and fold hero out. JJ would have raised pre.
That 5 probably changed nothing. Same story as flop.
I get check again and hope for a small bet again for value. I think you have to fold to the jam. An 8 could play the hand that way. If they really had the 8 would they over bet like that - probably not. But they could be tying to make an 8 look like a bluff. KQ QT could get here and bluff (but they should have bet more on the flop). Strange but not worth putting up my stack. Fold
River knowing it was a bluff
Villain has hit the following keys check, check, 1/4, 1/4, and all-in. Villain could be a fish playing a wide range. Problem is that range could include AJ, KJ, QJ, and 8x that have you beat.
If villain is not a fish they are not likely to value bet the river with a hand you beat. You have called twice so a weaker J or weaker pair are just going to check back. At this point bet out 1/2 the pot yourself to represent an 8 or AJ and take away their bluffs. If they come back with a jam then you can be pretty sure you are beat.