Bet sizing with JJ

[hopeful]

This is one of those hands where I think my strategy might have been wrong, particularly SPR and bet sizing.
I decided that the two limps were probably weak, low pairs or the like. The $700 bet made me start thinking of ranges, with this large raise I decided the range was AJ+, 99+, KQs with a 10% chance it was just a steal. Against this range my JJ is a coin flip.
I decided to raise thinking villain would shove if he had QQ+ and probably shove AK. If he did shove i intended to fold. I expected villain to fold the weaker parts of his range.

Villain called so I had his range as TT,JJ, and maybe AK,AQ. with the usual 10% chance of something else entirely.

After the flop I decided I was well ahead of his range but that I couldnt allow a free card so I pushed all in.
The reason for the post is that despite my getting his range right I didnt manage to get him out of the pot. Was it bet sizing that was wrong ?
Should i have played it different?

PokerStars No-Limit Hold'em, $7.00+$0.50 Tournament, 75/150 Blinds 20 Ante (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

BB (t1705)
UTG (t3095)
UTG+1 (t3705)
MP1 (t3015)
MP2 (t1155)
MP3 (t2785)
CO (t4520)
Hero (Button) (t5455)
SB (t7160)

Hero's M: 13.47

Preflop: Hero is Button with ,
UTG calls t150, 2 folds, MP2 calls t150, MP3 bets t700, 1 fold, Hero raises to t1650, 3 folds, MP2 calls t985 (All-In), MP3 calls t950

Flop: (t4990) , , (3 players, 1 all-in)
MP3 checks, Hero bets t1200, MP3 calls t1115 (All-In)

Turn: (t7220) (3 players, 2 all-in)

River: (t7220) (3 players, 2 all-in)

Total pot: t7220


Results in white below:
Hero had J, J (two pair, Jacks and threes).
MP2 had 9, 9 (two pair, nines and threes).
MP3 had K, A (two pair, Kings and threes).
Outcome: MP3 won t7220

[baudib]

Can't expect anyone to fold anything after putting more than half his stack in pre. Villain has right price to call with just overcards.

Board: 2d 3d 3h
Dead:

equity win tie pots won pots tied
Hand 0: 27.385% 27.39% 00.00% 78081 0.00 { AQs+, KQs, AQo+, KQo }
Hand 1: 72.615% 72.61% 00.00% 207039 0.00 { JJ }


So you got the money in while you're ahead, so it's not awful, but if your goal is to get villain to fold overs on a low flop, I wouldn't reraise preflop. Also, if you reraise preflop I don't see how you can fold JJ getting 3-1.