PL50, second barrel or not w\ TP OTT

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PL50, second barrel or not w\ TP OTT

Blinds: $0.50/$1.00 (6 Players) BN: $160.96
SB: $101.70
BB: $218.83
UTG: $171.69
MP: $561.41
CO: $104.83 (Hero)
Preflop ($1.50) Hero is CO with A 7 T K
UTG raises to $2.00, MP folds, Hero raises to $7.00, 3 folds, UTG calls $5.00
Flop ($15.50) 3 T 6
UTG checks, Hero bets $9.34, UTG calls $9.34
Turn ($34.18) 3 T 6 6
UTG checks, Hero checks

The main point of the post is to discuss whether 2nd barr is good play here, comparing to checkBack (and maybe provide some arguments for and against 3pl barreling OTR if called (on a river brick)

Villain here opens 50% and probably doesn't fold to 3b.
so, pre range is $FI50!$4bo3

with given ranges (#A is raising range) #B is x/calling range, when 6d hit the turn - we have (only) 36% of equity vs his flop calling range. In other words, the 6d hits his range rather hard

is it still reasonable to double barrel? Should we be more inclined to bet OTT with dd Draw or it becomes more of a call?
maybe you have some suggestions about flop ranges?
much reason to go for Checkback OTF? (recently came to conclusion that betting when you block TP on dry is pretty much always the best play), but would like to hear different opinions.

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