10/25 NL vs. total fish

[RaiseAndPray]

10/25 live NL, but playing more like 25/50 w/ regular large PF raises. Villain is a total fish and very predictable. My image is very LAG, and villain is willing to call me down light with any hand top pair or better. I hope this isn't considered TOO standard because I don't think it is, and brings up an interesting concept of reducing variance against fish.

Effective stack is $5k (200BB).

Villain raises in CO to $150, I call on button with TJ. It's heads-up.

Flop J T 3 rainbow

Villain bets $200, I raise to $600, he re-raises minimum to $1000. Now, don't worry about how I read his hand, just assume I KNOW he has QQ, KK, or AA (maybe the off chance of AJ, but I doubt it) with the line he takes here (like I said, 100% predictable).

My play in previous big pots with him has always been to wait for the best spots to put lots of money in because he is just THAT bad, I like to wait until he's in the worse possible situation. Is that backwards thinking or me just being over-cautious?

Anyway, I just call the min re-raise to see a turn (in case it's a counterfeiting 3 or some scare card). Should I have just jammed it all-in here (I guarantee he calls)?

But, I just call and turn is a 9. I don't like it for obvious increased straight outs now. He bets a measely $500 into a $2,100 pot. He has like $3.5k left. What now? I really just want to call, not because I think I'm losing (I KNOW for a fact I'm winning), but because I know he potentially has quite a few outs. Is this the right move, a call? Or should I just shove now so I don't risk a scare card coming on river and killing my action. Let it be known though that I don't think there are many scare cards that could make him fold river, but there might be some that make him only check/call a value-bet. I figure he has more outs than potential scare cards though, especially if he holds QQ.

Does this make sense? I'm trying to find the right balance of being aggressive and pushing when ahead, and seeing cards to try to minimize variance against the fish...any comments on this concept and/or hand appreciated. I'll post the hand results in a bit.