400NL, 5/10 blinds

villain (SB) is a very good LAG. he's either losing 5 BI's in 30 min or up 10 BI's whenever I see him. he's got about $3000

hero has TAG image and villain knows this. hero has $400

Preflop: Hero (CO) dealt A Q
+1 limps, +2 limps, hero raises to $55, SB calls, +2 calls

Flop ($170): T T 8
2 checks, hero bets $100, SB calls

Turn ($370): 6
SB checks, hero?

I have only about $250 left. I also have the A.
My question is do I push turn or take the free card and try to get value if I hit on the river?

If I push turn, what is in his likely calling range besides flushes?
If I push turn, what do you think are the chances I get called?

If I take a free card and it's another heart, what is in villain's calling range if I shove? are small flushes or Tx in that range?

I know this is all read dependent. But maybe you can help me figure out what range of hands villain might play this way-- c/c preflop, c/c flop, c turn...?

I push

EDIT: and your subject is wrong.

I pushed and got called by JJ.
I obviously didn't think he would play this hand that way. Just wondering if I misplayed the turn

i dont c how you can cbet that flop into 2 ppl and not shove any turn.
he wont have flushes there imo coz he play those fast on flop. mainly mid pairs/8x..
prolly he had read on ur barreling...