good fold or weak? 2/5 live

2/5 NL local casino.
Play is pretty soft. Ive been ultra tight due to real bad cards.
The lady in this hand is dangerous, since she knows how to play deepstacked. Havent seen too much showdowns by her, but seems at least to be aggressive.

I have 600$
She has me covered

I open to AdJh 20 after one limper, who habitually limps and folds to raises in MP.
The lady calls on the BU.limper folds.

Flop: J82 all clubs, i bet near pot, she calls quickly.
Turn 2h I bet 2/3 pot to 120, she raises to 240???


I finally muck and feel like a weak sucker.