I played this one horribly. My opponent is also typically pretty quiet, so I think I need to check-fold after my bet, which should have been on the flop. But I do think you have to bet this hand:

Poker Stars
Pot Limit Omaha Ring game
Blinds: $1/$2
8 players


Stack sizes:
UTG: $389.15
UTG+1: $70
MP1: $155
MP2: $389.40
CO: $438.50
Button: $317.40
SB: $79.50
Hero: $208.50

Pre-flop: (8 players) Hero is BB with
UTG folds, UTG+1 calls $2, MP1 folds, MP2 calls $2, CO calls $2, Button raises to $6, SB folds, Hero calls $4, UTG+1 calls $4, MP2 calls $4, CO calls $4.

Flop: ($31, 5 players)
Hero checks, UTG+1 checks, MP2 checks, CO checks, Button checks.

Turn: ($31, 5 players)
Hero bets $29.45, UTG+1 calls $29.45, 3 folds.

River: ($89.9, 2 players)
Hero bets $86.9, UTG+1 calls all-in $34.55.
Uncalled bets: $52.35 returned to Hero.

Results:
Final pot: $159

Correct line imo is pot the flop, then check-fold ???

Looks like the results aren't included: Villain has KK here.

One additional comment: If I just had trips here or had JJ, I think this might another spot for a probe bet of something like $14.

Essentially, these paired boards have several groups of hands: Trips, quads, and various full houses. I think trips are still bettable, just relatively weak. After that, I think you want to check unless you at least make the nut underfull.