My sister is refusing to talk to me?

[shescaptainjack]

I have an older sister who is refusing to me. In a nut shell what happen was I'm on a diet because my parents constantly shout, be cruel and bully me because of my weight when I don.t So I decided to calorie count. I have 2000 calories a day. I was eating a tuna pasta salad and I left the empty plastic dish which the pasta was bought it from ASDA on the desk in my study. I have to big dogs who can easily reach up to get things of my desk (and frequently do) in the study. Anyways my sister found the salad tray on the floor in the kitchen and assumed I fed the dogs the salad to avoid eating. She told my mum and dad who believe her over me because like week I said to my mum "yes I ate some of the crisps" when they think I should of siad "yes mum I ate 3/4 of the crisps" so was therefore lying so don't trust me (even though they'd of gone off on an another your so greedy and fat rant if I said that). yesterday she was verbaly abusive but know she's not talking to me. We've never really get on and I can see us in future only meeting at family events but I want to leave on good terms. In the past when shes stopped talking to me I've tried talking at her about my day etc or asking questions Like "please pass me that thank-you" but when she started talking to me again she'd tell me that she continued to not talk to me for longer than she has planned because she felt like I was needy and crumbling apart without. We don't really spend time with each other outside the house unless its with each others friends. I don't really like my sister but i'd rather be able to tell any friends or future kids( and myself) the reason I don't see my sister is because of work commits etc not because we hate each other. I don't like her but I believe that whilst we life in the same house we should be polite and friendly to each other and try to do stuff as a family. What should I do? I want her to talk to me but not seem like i'm needy.
Thankyou for your time.