Help with JJ

[theDetroitKid]

Playing 100-300 buy-in ring NL at a B&M indian casino buyin NL with 2-5 blind structure.

With 9 players, I am on the button preflop with JJ.
UTG folds, UTG+1 folds, MP1 raises to $20. MP1 is a loose aggressive player who was been raising 4x the big blind all night with A9, A10, AJ, KQ, KJ, K10, Q10, and other marginal hands.
MP2 (who is friends with MP1 and has been playing almost the same style(LAG)) all night calls.
MP3 folds.
LP1 and LP2 also call (both of these players are good tight agressive players).
Now it is my turn to act on the button with JJ and four players already in the pot for $20 dollars each.

Pot is at $80 and I have about $120 left in my stack. I decide I don't want to play JJ against 4 opponents and need to either raise or fold. Figuring that MP1 & MP2 have been raising preflop with marginal hands all night and that if LP1 or LP2 (both TAGs) did not reraise them I was probably in good position for a raise. But how much? Should I raise $40 of my $120 to see a flop and then decide either to push or fold? Should I push and try to win the pot right then? I decided that if I pushed I would probably get all to fold and win $200 with my $120 push or be going against two overcards from one of the MP(loose) players and be at least a 55-45 favorite to win $300 with my $120 push. I went ahead and pushed.

Did I play this correctly?
Am I being to aggressive preflop with JJ in this situation?
Would anyone recomend calling in this situation and if so how would I play it? Hope undercards flop and then push?

Thanks, Results are below in white
theDetroitKid

<font color="white"> I push allin.
MP1 (the original raiser calls).
The three others fold.
MP1 shows KQo

Flop: 7-6-6 (i cant remember suits, but they are unimportant)
Turn: 10
River: Q!

I lose and MP1 collects the 300 in the pot. </font>