My girlfriend is "sick" I feel like I should be pushing her into independence.
Is there a problem with her not being independent?
Yes, I don't like how dependent on me she is
It can be hard to be the one that people depend on, so it is okay to want your girlfriend to be more independent. It will make you both happier to live some of your life apart.
I just wish she would stop relying so much on me.
It's normal to feel like you are important to your partner but being able to have separate interests and spending time apart can make for a happier, healthier relationship.