The only time that warrants avoiding the big stacks is in tournament poker. In cash games you target everyone the same. The reason big stacks avoid each other in tourney poker is you can't just re-buy. In cash games I want the big stack to play with me as it increases my impied odds. If the big stack is as LAG as you read, then tighten up a little b/c of your position to his right and punish him with your good hands.

I think you fold to that turn raise as well. He isn't cold calling 10 on the flop with nothing but a draw unless you have tilted him, and he hates you. I think he likes the Q and has the A or K of s or he has you already with trip 3s or 9s.(smooth call, turn raise reaks of trips).
The only question I have is: Would you push your JJ that hard into a turn raise against anyone else? Is your read that accurate or are you tilting for this guy a little? Wait for a better situation and take his stack.