[50NL 6max] Flopped Flush OOP - Line Check

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[50NL 6max] Flopped Flush OOP - Line Check

Blinds: $0.25/$0.50 (6 Players) MP: $62.55
CO: $51.56
BN: $110.09
SB: $56.30
BB: $57.43 (Hero)
UTG: $37.68
Preflop ($0.75) Hero is BB with 8 6
UTG folds, MP raises to $1.50, CO folds, BN calls $1.50, SB folds, Hero calls $1.00
Flop ($4.75) 9 5 K
Hero checks, MP checks, BN bets $1.50, Hero calls $1.50, MP folds
Turn ($7.75) 9 5 K 6
Hero checks, BN bets $2.25, Hero raises to $9.46, BN calls $7.21
River ($26.67) 9 5 K 6 A
Hero bets $44.97 and is all in

I'm wondering what you think the best course of action is on all streets post-flop. Here's my thought process.

Villain is seeming like a rec. he's running 34/21 with 7% 3bet over a couple hundred hands. No specific reads.

Flop ---> XR and XC are both viable options. XR is a bit too aggressive at this point as if we face a flop 3-bet, we're in a very tough spot. So I slightly prefer XC. Plus we will have a lot of hands that need protection and 86s does a good job protecting our checking range.

Turn ---> At this point, is there any option other than to raise when we face a bet this small? It's setting up a really poor SPR for the river to get the money in from the IP player's perspective. His bet looks weak and so from his mind, it might induce some spazzes from me when I have As or a hand like 8s8x etc. So right now I strongly prefer XR and build pot as we can be perceived to have a lot of weaker hands that are turning themselves into a bluff vs a weak looking bet that looks like it's trying to buy a cheap check on the river.
.
River ---> With a ~1.8:1 SPR, does anyone prefer a different sizing? Perhaps 3/4psb? To me shove or check seems like the only option given how the hand played out. The Ad is not a great card in the sense that my AsX bluffs now have showdown value and are probably never shoving. So we have less pure bluffs.

Thoughts on all streets?

As an extra,
How would you play a set vs the same sizings from villain?

Thanks

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