I'm sorry to hear that, it's a very tough decision, but I'm very glad that your sister has someone like you that cares for her. Have you ever sat down and tried to talk to her, just one on one? You and her, and that's it? Let her know that you aren't threatening her in any way, shape, or form, but you just want to know how she feels...?
Right now, you said she doesn't want help... but that in and of itself may be a call for help and she doesn't realize it. See if you can talk to her and understand how she feels... I don't know how close you are to your sister, but you may be one of the best people to talk to her.
If you try and talk to her with more than one person, then she may feel like she's being 'attacked'. If anything, she may feel horrible already, especially if she feels that she's not only hurting herself but those around her as well... does that make sense? For that reason, I suggest you just sit and talk with her one day, one on one, and see if you can get somewhere. If you can, bring up why she doesn't want to go to your family's counsel, and whether or not she's prefer to see a professional on her ~own~, just one on one. As well, ask her what she wants you and your parents to do, and how you can help her out. If she says she doesn't want help, then make sure she knows that when she ~is~ ready to talk to any one of you, she can. Sometimes letting her know that no matter what, someone will always be there to give a helping hand, can make all the difference :).
Try to let her see that SHE has the decisions, and that no one's forcing her in to anything... but merely trying to guide her to trying to find her own happiness. It's hard finding a good medium, but you need to search for it, right? If you can, maybe you can suggest to her to write things via notes... or if she has trouble talking to you in person, she can always contact you through e-mail if that would be easier for her to communicate. Throw ideas out there, maybe one of them will be attractive to her :).
And from there, just keep being supportive. Having her seek professional help will be ideal, but if she doesn't want to go, then she won't benefit from it anyway. So tell her that the option is always there for when she's ready. Maybe even mention that you're worried you're losing your little sister, and that you would give anything to see her smile again. Other than that, the choice falls on her shoulders... not only because of her age, but because SHE has to decide when she's ready for a change.
I don't know if you live with her or not, or if she lives with the family... but if she's also that concerned about her weight, ask her if she's interested in going on a diet with you and the rest of the family. Just a diet of eating healthy meals and healthy portions and the like. Maybe that might be easier for her? Or maybe if she wants to go speak with a nutrionist to understand how to eat and be healthy and not gain weight? I'm just trying to throw some ideas out there, because the more options you have, the better you can assess what's best for you. Those are just a few things that may or may not work, but are worth a mention.
I wish you and your family the best of luck. It's great that you all care about her, and hopefully she can find her reason to get things back on track for herself :). Best of luck to you and your family, and I hope you find a solution that benefits everyone :).