[SossMan]

I would flat call preflop here almost every time if i didn't have a read. You have position on him. Of the three players behind you, you have position on two of them. You have a hand and a stack that would hate a reraise all in preflop. You keep the pot manageable on the flop in case it comes Q rag rag (familiar). did I mention position?

that being said, you now are in a real peach of a spot on this flop. he's going to check to you no matter what, so you can't really read that check as weakness. Statistically, you probably still have the best hand. There are a few hands that most players would play that way preflop that include a Queen (AQ,KQ,QJ). There are a ton of hands that he would play that way that you are beating (AK, underpairs, etc...)
I think an argument can be made for pushing, betting out 1000 and folding to a reraise, checking behind and folding unless you spike a set on the turn.
I would probably push, since you are likely ahead, but don't want to get bluffed off the turn. You really don't want him assuming his JJ is good on the turn, if he would have folded to a flop bet.

Your preflop reraise put you in a tough spot.

-sossman