My sister is concerned about her weight and I wanna help her..?

My 11 year old sister is concerned about her weight. every time she looks at any of her friends that are skinny, she becomes insecure because she thinks she has a fat belly and fat thighs. She is the average height of any 11 year old, and weighs 87 pounds. her highest was 93, and her lowest was 84. her weight keeps jumping in between 87-90 because every time she loses one pound, she rewards her self with eating junk food then gains 4 pounds the next day, and goes back to eating healthy. she really wants skinny thighs. when i tell her she's perfect the way she is, she yells at me to shut up and help her lose weight. I want her to be happy, so im helping her lose weight. She usually drinks a huge cup of milk every morning (our parents force us to) for breakfast, skips lunch, and for dinner she usually haves anything on a medium sized plate. This is what she had for dinner the past week:

Monday: 7 small pieces of fried chicken and rice

Tuesday: Rice and one hotdog with no bun

Wednesday: Rice and tofu

Thursday: 4 fish sticks

Friday: about 5-8 pieces of vegetable dumplings(idk what to call them, the dumplings with soup)

and..we havent gotten to the weekend yet. Is what she's eating too much or does she need to eat less? and..is her weight ok? I dont know how tall she is, but I know she's the average height of any 11 year old and 87 pounds right now. She's always checking out her legs and belly because she's so paranoid. She has to admit she think her lower arm looks skinny, but doesnt care about her arms.

I know this is a dumb question, I just really wanna help her