I will not give myself the check
Villain
I do not like his play. He took down the pot but put too much at risk to do so in my opinion.
Flop
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+.
Turn
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.
River
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.
Hero
Pre flop
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.
Flop
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.
Turn
That 5 probably changed nothing. Same story as flop.
River
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.