Try not to feel so bad, because you're not the first person to feel so lonely, and you definitely won't be the last. As much as you may think that no-one loves you or no-one cares about you, that's so not true. Your mum might just be concerned about your weight, she wants you to be healthy and will always love you no matter what. She might not understand your situation which is why she might not be so sympathetic, but I'm sure she cares a lot for you. Maybe she doesn't think you're putting enough effort into maintaining a healthy lifestyle, and whether or not you want to, you will always be her child. You don't need to go on freakish diets and run for miles. Small amounts of exercise and some salads, fruits, vegetables can all help to make yourself healthier whether or not you end up losing weight. The most important think, in my opinion, is that you should be happy about who you are. Be happy with yourself, because we are all made one way or another, for better or for worse. If you want to lose weight, you can, but you have to maintain a positive attitude and keep at it even when you feel like it's going nowhere. These things don't change in a few days, and you can't expect to train for hours daily. Moderate exercise and a balanced diet can and will make you healthier, but it takes a while, even many months. Be prepared to do it. Ask your mum for help, and no doubt she will try to help you because she does love you and ultimately wants what she thinks is best for you.
Cutting is not the answer, and doesn't solve anything. It just creates more problems for you and for your friends and family. I'm sure you have friends, and even if you think you don't, you can still make friends. It's not easy at first, but it can be done. Be sociable, go up to people in school and get chatting in conversations. Make yourself known, be approachable. Have a funny and laid back attitude, and soon enough people will take notice and will talk to you. But you have to try and put in the effort to, because people don't usually just come up to you. Make jokes and really take part in class discussions so that people can see what you're like.
It's good that you have your gran that you can talk to. She knows you and is there for you, but you said that's not enough, and that's true. You need someone new that can take a clean perspective to the situation. This is why I'd suggest a counsellor, even at school if you have one. These people are trained with these situations and can help you find what's causing the problem. They can suggest new and novel ways to deal with your problems, and if you want you can even get your mum involved. It's great to be able to talk things out with someone else and get them to pose questions or suggest ideas that can make you think of yourself in a different way.
I hope this has helped, just remember to keep strong and don't cut, because there is hope, and you will reach the end of the tunnel.
- Balazs