I haven't been at this table terribly long (I think this is the 30th hand or so) and don't think I've played vs this specific villain (running 31/7.5/1.5 through 200 hands of datamining) before. Here are the significant hands before this one:

He is not the villain in this one, but he's at the table.

No Limit Holdem Ring game
Blinds: $2/$4
5 players
Converter

Stack sizes:
UTG: $124
CO: $1142.40
Button: $435.30
SB: $216
Hero: $800

Pre-flop: (5 players) Hero is BB with 7 Q
2 folds, Button raises to $12, SB folds, Hero calls.

Flop: 3 4 K ($26, 2 players)
Hero checks, Button bets $12, Hero raises to $40, Button raises to $128, Hero folds.
Uncalled bets: $88 returned to Button.

Results:
Final pot: $106

Villain is the UTG raiser here:

Absolute Poker
No Limit Holdem Ring game
Blinds: $2/$4
5 players
Converter

Stack sizes:
UTG: $1142.40
CO: $485.80
Hero: $804
SB: $120
BB: $192.20

Pre-flop: (5 players) Hero is Button with A Q
UTG raises to $16, CO calls, Hero raises to $48, 2 folds, UTG calls, CO folds.

Flop: 4 T 5 ($118, 2 players)
UTG checks, Hero bets $92, UTG calls.

Turn: 2 ($302, 2 players)
UTG checks, Hero bets $230, UTG folds.
Uncalled bets: $230 returned to Hero.

Results:
Final pot: $302

Okay, now onto the actual hand in question:

No Limit Holdem Ring game
Blinds: $2/$4
5 players
Converter

Stack sizes:
UTG: $408.80
CO: $287.05
Hero: $935.40
SB: $287.62
BB: $1106.40

Pre-flop: (5 players) Hero is Button with 8 7
2 folds, Hero raises to $16, SB folds, BB calls.

Flop: 4 T 5 ($34, 2 players)
BB checks, Hero bets $29, BB calls.

Turn: 3 ($92, 2 players)
BB checks, Hero bets $80, BB calls.

River: 6 ($252, 2 players)
BB checks, Hero bets...?

His stats indicate he's pretty passive. You need to bet to be called by a 1 pair hand here. I think something like $150 to $175 will work as long as he's not smart enough to go "he's obviously value betting, so I should fold."

If he is that smart, make a bluffy looking bet. I mean, a lot of the time he shows up with no pair here and you can't get value anyway.

If you think he is frustrated and looking to make a big call, make a big bet. I would put in at least 190. I really don't think he would check anything but the nut flush to the river, and I don't think he'd check the nuts on the river. I am confident you are ahead, and it looks like he's willing to make a big call on the river.

I'm 99(edit: +.99) percent certain here I'm ahead. I'm definitely not concerned about getting check-raised and if that happens, I pay him off. I'm more concerned about putting the right amount in the middle. That river makes it a tough hero-call with a lot of one-pair hands, too.

I'm betting about $200 here. I think it's most important to get a call of $200 with his normal calling range than to make it $150 and try and get a weird hand like 99 to call.

I think if he is willing to call with stuff like As10x, sets, naked 7, etc. that he'll call $200 just as often as he'll call $150. I don't think it's likely he calls you here though, he plays passive and played passive here. Seems too likely to me he just has one big spade and one card that is not connected to the board. If he does call I think his most likely hands are baby flush or Xs10 where X is J-A.

I'd bet $201.

I think the same.

I like $250 for value. He's been calling down PSBs, so why not make another? If you want to spoof a bluff, shove.

I'd bet $210. Obviously he's almost never calling you down with just one pair after that river card, so make a bet he's going to pay you for if he has a straight, set or two pair.

Hope he has A 7 x

$150-170 but i like $150