NL25z Facing triple barrel in 3b pot with connected board

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NL25z Facing triple barrel in 3b pot with connected board

Blinds: $0.10/$0.25 (6 Players) BN: $42.99
SB: $27.50
BB: $25.25
UTG: $11.62
MP: $12.60
CO: $38.21 (Hero)
Preflop ($0.35) Hero is CO with 4 4
2 folds, Hero raises to $0.63, 2 folds, BB raises to $2.01, Hero calls $1.38
Flop ($4.12) 6 7 9
BB bets $2.71, Hero calls $2.71
This is a board that should be bet big very infrequently by BB, also seeing that we have more 88 and other pair+straight draws in our range (in theory he should probably also have those SC, but they mostly a linear range with some suited Ax from my experience). So Im already not happy here and with my assumptions (him betting with all sorts of overpairs, some AdKx or AxKd), we are pretty break even here with 44. With my assumptions, solver liked to call here at least with 55. So Im already considering to fold here in hindsight
Turn ($9.54) 6 7 9 5
BB bets $6.29, Hero calls $6.29
Picking up an OESD (prob with some reverse implied odds on some outs, due to him being able to play his one card diamonds like that), I just dont see what bets as aggressively here from his value hands (maybe some top sets or overpairs+FD he got married to) .. I see everything halfway reasonable checking here to be fair apart from the absolute nuts.
River ($22.12) 6 7 9 5 J
BB bets $14.24 and is all in, Hero folds
After him jamming, I assume this will be a very infrequently bluffed board by population and folded.. plus didnt like to herocall here only to be shown some funky overpair+FD that overvalued itself
Final Pot BB wins $22.12

I nodelocked this in a solver and it likes to raise with all sort of slowplayed sets, twopairs and flushes OTT. My line would have been taken with 55 at least. River is being called with some slowplayed lower twopairs, every other call is pretty breakeven

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