I know how you feel (: I'm 17, turning 18 in a few months and my family is the same way. They eat nothing but crap food, nobody works out (my dad will do it for two days and then stop for months), and everyone is 'too busy' to fix it. When I was 12, I was 85 pounds. When I was 13, I was 150. It was a big jump, and I used to beat myself up over it. Then I realized the muscle gain and puberty had something to do with it as well. You have to keep in mind that your chest (not so much me) and butt (muchhhh more me) weigh more than you think. So keep that in mind as you lose or gain weight (: You're still growing. That being said, DON'T STOP EATING. But don't eat junk food either. Give her a list of the foods you'd like, and learn how to cook. That may have been the most important part of weightloss for me. I love tofu, salmon, and thin-chicken breasts covered in herbs and wheat bread crumbs (homeade). Eat five times a day, but make them little meals. I like having sandwhiches (wheat bread, turkey, lettuce), but I workout a lot, so I assume it makes me hungrier. You can have a handful of chips a day, or a chocolate or two. But don't over do it. Also, my mother doesn't let me have a scale. So, I've learned how important measurements are. You can weigh 105 pounds and have a bigger waist than a person who weighs 130 pounds (I confirmed this first hand yesterday when we were comparing measurements

Good day for me). Working out is also very important. And it's important to make it a lifestyle. Run. Run run run. Crunches don't do crap if you have fat on top (trust me -.-; I've tried). Run in the morning before she leaves, or run at night when she gets home, if you don't want to be seen. Get up and move around a lot. Clean the house, dance to music, do jumping jacks every 10 minutes. Do something other than sitting there. In fact, sleep if you have to. It burns more calories than just sitting. One last thing; drink water. It's free, and it's the best thing you can do for yourself. You'll feel full more often, eat less, and then rid your body of toxins.
Good luck, love. I've been in your shoes; I promise it'll get better (: