Hello,
Villian unknown

raise flop to put pressure on villian + gutter and cards may improve
turn barrel standard i think
river bet to tell a story betsizing?

PokerStars - $0.25 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: $25.73 (VPIP: 16.00, PFR: 10.00, 3Bet Preflop: 5.88, Hands: 50)
SB: $52.31 (VPIP: 27.27, PFR: 18.18, 3Bet Preflop: 0.00, Hands: 11)
Hero (BB): $59.64
UTG: $25.00 (VPIP: 23.81, PFR: 11.90, 3Bet Preflop: 0.00, Hands: 45)
MP: $36.66 (VPIP: 10.81, PFR: 2.70, 3Bet Preflop: 0.00, Hands: 42)
CO: $49.26 (VPIP: 33.33, PFR: 20.00, 3Bet Preflop: 0.00, Hands: 15)

SB posts SB $0.10, Hero posts BB $0.25

Pre Flop: (pot: $0.35) Hero has 6 7

fold, fold, fold, fold, SB raises to $0.75, Hero calls $0.50

Flop: ($1.50, 2 players) 4 3 2
SB bets $1.07, Hero raises to $3.25, SB calls $2.18

Turn: ($8.00, 2 players) 6
SB checks, Hero bets $5.25, SB calls $5.25

River: ($18.50, 2 players) J
SB checks, Hero bets $12.25, fold

Hero wins $17.67

I'm check back ott since now I'm have pretty decent sdv.

But does a checkback withdraw all sets out of my range which i will fire turns with a 100%?
What is your line by facing a near ps bet on river? Without reads you need to fold nonetheless, could be villian will bet any2 without showdown value and try to steal river?

Preflop I would rather 67o as a 3 bet bluff as I don't think it works that well as a call, any thoughts?
You may want to bet small on turn, around 2 thirds, something that you could do with your sets. And check back river, not needing to face a river bet since we have the control on the hand.

You are looking for check/check vs hands like A4,A3,A2,47,73 etc and sometimes check/check vs Ax.

Obv fold to a river bet. Just play your hand like a hand with good sdv. Villain shouldn't turn into a bluff many sdv combos.

AP if you bet turn then you are obligated to bet river representing a set/str8. But I rather bet really big - close to the pot.

This seems fine to me (though I'd probably tweak the sizings a little). This is probably going to be the worst hand in your range by the river.

I don't think you should be firing turns with all of your sets 100% of the time. All of the 5x you'd also raise the flop with improved, so sets are going to be closer to the middle of your range. Not to say that you shouldn't bet any sets, but betting all of them doesn't seem like a great idea to me.

So, it shouldn't withdraw all sets from your range, but that shouldn't be a problem anyway.