More Overly Thin PLO Value Betting

This is a pretty consistent problem for me:

Poker Stars
Pot Limit Omaha Ring game
Blinds: $2/$4
6 players
Converter

Stack sizes:
UTG: $302.70
UTG+1: $361.75
CO: $338
Foucault: $400
SB: $76
BB: $304

Pre-flop: (6 players) Foucault is Button with
2 folds, CO raises to $12, Foucault calls, SB folds, BB calls.

Flop: ($38, 3 players)
BB checks, CO checks, Foucault bets $33, BB calls, CO folds.

Turn: ($104, 2 players)
BB checks, Foucault bets $80, BB calls.

River: ($264, 2 players)
BB checks, Foucault bets $261, BB calls all-in $179.
Uncalled bets: $82 returned to Foucault.

Results:
Final pot: $622

He won with [6h 7h 4d 2s] (a full house, Sixes full of Deuces). Granted he made a pretty implausible full house, but there really aren’t second best hands for him to have here. Flopped two pairs either boated up or got counterfeited, draws missed (unless we are chopping), and the 6 has to be a scared card if he has a K. The 6 in my hand made me a bit more confident, and his failure to raise the flop or turn made me think he didn’t have a set, so I was thinking he’d have to hold the case 6 to make a boat. But I wasn’t thinking enough about which worse hands could call me.