This hand makes my head spin. Villain is a good TAG regular at 23/21/3.

I am BB. My range after calling the turn vs this guy on this board is 66/77/JJ/QQ/AhKh/AhQh, virtually never anything else. There's only 4 combos of 66/77 and 14 combos of the rest, so if I fold everything but 66/77 then I'm folding 78% of the time, but I only need to fold more than 61% for a bluff to show profit.

What's the correct action with JJ/QQ here? Flip a coin? Does that make him shove AA/KK for value?

Button ($979)
SB ($410)
BB ($1000)
UTG ($2305)
MP ($2432.50)
CO ($1972)

Preflop:
UTG raises to $35, 4 folds, BB calls $25

Flop: ($75) 6, 7, 6 (2 players)
BB checks, UTG bets $55, BB calls $55

Turn: ($185) 3 (2 players)
BB checks, UTG bets $150, BB calls $150

River: ($485) 3 (2 players)

BB checks, UTG bets $2065 (All-In), BB?

840 for me to call...