You should definitely talk to your doctor. It may not be a good idea to put her on HORMONAL birth control if she is so young, since she is still developing and it will affects bones and things. The depo shot has a very high risk of causing osteoperosis already, so is probably not good for a teenage girl. Also, all hormonal bc types work differently for everyone, it is not an exact science. Talk to the doctor, especially if there are weight concerns, history of depression/mood swings, etc. It will help them make the right decision.
That's a hard one. Many hormonal birth control are designed for fairly average sized women. Something like an IUD or maybe those sticks they put under the skin may be what is suggested. I really don't know but would like to know what is perscribed, out of curiosity. Good luck to your sis, and I'm glad she could talk to you, and had the forsight to start protecting herself.