Dd is 13 and very lazy, she has Aspergers and a lot of sensory issues around food but is also very stuburn, won't attempt to try new foods, won't go near a vegetable and will hardly touch fruit, she also won't eat meat. Her diet consists of cheese, bread, pizza, chips and blueberries. She also has hyper mobility and hypertonia so gets very painful joints, she has been advised that this could improve with exercise but she refuses to do any and argues that it hurts her legs, if I make her walk a small distance she cries (not in pain, just because she doesn't want to do it), we have a large garden with a trampoline but she won't use it.
She has just got up to get ready for school and the trousers I had bought her won't go over her bum, the school she goes too asks for specific brand of trousers and I none of the styles will fit her, she's quite short, 30" waist but large bum. I have just had a talk to her about eating better and doing more exercise, not really because of the trouser situation but because m worried about her long term health. I think 💠have upset her but I just don't know what to do 
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I have tried only giving her healthy food but she just refuses to eat it. She has free school meals so can buy what she likes at school, the school serves pizza and it's the only thing they serve that she will eat, she will then buy herself a cake to go with it, school provide healthy options but she says she doesn't like them. Her diet is so limited that it's hard to extend it (I have been trying for years), we make our own pizza but she won't contemplate adding new ingredients so will just have cheese on it. I make my own chips using fry lite but she complains about them. It took me years to get her to eat the inside of a jacket potato and she will only eat it if covered in cheese. I am tempted to remove all cheese from her diet but then she won't eat anything.
I'm worried that dd will become overweight, she already gets bullied and called 'weird', 'geek' etc.. and she gets bullied for being slow on her feet due to her hypermobility. I don't want another reason for her to get picked on but she doesn't see it that ways and says she doesn't care if she gets fat and doesn't care if she ends up in a wheelchair because of the hypermobility (which will happen if she gains too much weight), she makes jokes about owning a mobility scooter and stair lift in the future.
What can I do? At the moment I am trying to bribe her into trying new things, we have a chart and she gets money towards a game she wants if she tries something new, we have been doing this for a month and she's only tried 2 new things and hated them both.