PokerStars - $0.02 NL - Holdem - 8 players
Hand converted by PokerTracker 4

Hero (BTN): 122.5 BB
SB: 144.5 BB (VPIP: 16.92, PFR: 13.85, 3Bet Preflop: 0.00, Hands: 66)
BB: 100 BB (VPIP: 30.43, PFR: 17.39, 3Bet Preflop: 0.00, Hands: 23)
UTG: 100 BB (VPIP: 8.70, PFR: 9.09, 3Bet Preflop: 0.00, Hands: 23)
UTG+1: 129.5 BB (VPIP: 62.50, PFR: 31.25, 3Bet Preflop: 28.57, Hands: 16)
MP: 100 BB (VPIP: 8.70, PFR: 8.70, 3Bet Preflop: 4.55, Hands: 69)
MP+1: 196 BB (VPIP: 18.75, PFR: 15.63, 3Bet Preflop: 7.14, Hands: 32)
CO: 41 BB (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 12)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has K J

fold, fold, fold, fold, fold, Hero raises to 2.5 BB, fold, BB calls 1.5 BB

Flop: (5.5 BB, 2 players) K Q 6
BB checks, Hero bets 4 BB, BB calls 4 BB

Turn: (13.5 BB, 2 players) 9
BB checks, Hero checks

River: (13.5 BB, 2 players) T
BB bets 9 BB, Hero raises to 19 BB, BB raises to 93.5 BB and is all-in, fold

BB wins 49.5 BB

This board has run out pretty bad against this villain who's turning out to be quite loose passive. I checked back the turn intending to call/value bet the river with my top-pair hand. But then I make the straight so I thought that I can get value from two-pair and sets that the villain is bad enough to call with.

Is this OK or is it better to just call behind and make notes on what he had?

Also how does the mathematics work in spots like this? Like, if we assume he only ever calls/folds with worse, or shoves and we fold.

Obv when he jams the river I'm way behind and it's an easy fold every time.

I would only raise/fold otR as a bluff, but never for value.
In this hand, I would simply call the riverbet. Although, if he's really passive we're probably beaten, so even calling is a close one. But we're definitely not strong enough to raise. We're only getting called/raised by better.

About the mathematics when facing the shove:
Pot = 126 BB
To call = 93.5BB
We should be right 42,5% (93,5/(126+93,5))of the time to make this call.

Do we have 42,5% equity vs. his shoving range? I don't think so.

Vs V's initial river-bet, we need 41,8%. Vs his wider betting range, it can be a good call.

bet turn on the smaller side
ap call river