Hmmm, just going by what you have told us thus far. I say bring your kitty to the vet and get a full evaluation done on her. Ask about the claw, and her weight problem.
It is very unhealthy for cats to be over weight, just like humans, it can cause several health problems, as well as shorten their life span.
Talk to your vet about a good diet to get her on, and hopefully ovetime you will start to see your kitty slim up and look/act healthier!
I've only ever met one cat who had the claw problem, but was with all of her front claws, for some reason she couldn't retract them. She wasn't my cat and I never really found out why she was this way. But hopefully someone here will have a little more info for you while you get your next vet appointment.