blind war

Villian is 40/22/2.7, over 36 hands
Full Tilt No-Limit Hold'em, $0.50 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

BB ($50)
UTG ($44.25)
MP ($50)
CO ($213.90)
Button ($138.05)
Hero ($79.75)

Preflop: Hero is SB with Jhttp://www.flopturnriver.com/phpBB2/...es/diamond.gif, Jhttp://www.flopturnriver.com/phpBB2/...miles/club.gif.
4 folds, Hero raises to $1.75, BB calls $1.

Flop: ($3.25) 6http://www.flopturnriver.com/phpBB2/...iles/spade.gif, 5http://www.flopturnriver.com/phpBB2/...es/diamond.gif, 6http://www.flopturnriver.com/phpBB2/...es/diamond.gif (2 players)
Hero bets $2, BB raises to $9, Hero calls $7.

Turn: ($21.25) 9http://www.flopturnriver.com/phpBB2/...iles/spade.gif (2 players)
Hero checks, BB bets $12, Hero calls $12.

River: ($45.25) 7http://www.flopturnriver.com/phpBB2/...miles/club.gif (2 players)
Hero checks, BB bets $27.5 (All-In)

I'm thinking this hand plays easier if I just 3-bet the flop. Turn is just grusome with 1/2 pot behind.

I don't 3bet flop. Hell, I'm not sure if I call the flop. That's quite a hefty raise there. The pot is now bloated and you'll have to play JJ OOP the rest of the way for stacks.

Check/push turn.
Villain's range is massive here.

Isn't villains range all over that flop?

This is a very tough spot since villain's range hits this flop huge.

6x, 78 and the killer 56 or 55 are all possible.

The only thing you beat is the odd overs + flushdraw. I think I like leading the turn since the big draws will typically flat call and the big hands will just shove and you can easily fold.