How to Motivate a Teen to Develop Good Habits

Hi everyone- I'm hoping someone out there might have some advice for me. My 15 year old daughter is obese. This is not at all about appearance... I'm really concerned for her mental and physical health. She eats large amounts of unhealthy foods, sits on the couch as much as she possibly can, and is quite depressed. I'm really concerned that she is setting herself up for a lifetime of bad habits, and with our family history, that will undoubtedly affect her quality and quantity of life. I'm doing what I can in terms of setting a good example, keeping lots of healthy, whole foods in the house, and being supportive by offering to sign her up for literally ANY activity she would like to try (without judgement or pressure!), but she seems so stuck, and fearful of stepping outside of her comfort zone. Has anyone dealt with this, and is there anything more I can do to motivate her to get more healthy? I love my daughter, and just want what's best for her.

Thanks in advance!