Eating Disorder getting in way of relationship w/ sister

NEED SUGGESTIONS.. So, my sister (16 months older than me) and I have never had the sister relationship that i wanted with her. It always sort of felt strained and there are many reasons for that which i wont bore you all with by going into detail. However, I put myself out there right before Thanksgiving and told her i wish that she and i had been closer and i always wanted her to be my best friend. I told her how i always admired her strength and determination and that, silently, she was more of a role model for me than my own parents. (Shes super smart, was voted sexiest senior in high school, and one of the popular, she is also a self made millionaire). I didn't know what she'd say but i was prepared to hear anything... Except that she felt the same way about me!!! ???????? Anyway, we have decided to get together once a month now to hang out and try to cultivate our relationship... The ISSUE IS... She suffers from an ED... In her early years it was more of an anorexic thing.. Then it became more bulimia.. Now, she has just given up on trying to keep the weight off (she fluctuates from a size 2 to 22- seriously) and just eats... And eats poorly and doesn't work out. I know she is very depressed about this and over the summer had disclosed, on a whim, having gone to an ED clinic for 3 years and gave up as it didn't help her. she kept this a secret from the entire family. She would like to get together and do food related monthly visits and i am hoping to come up with alternatives. Going out to eat, with just her will be awkward for me because I know she is used to me usually being heavier than she is. i also know i will want to make healthy choices and will feel compelled/tempted to make poor ones when i am with her. While i would like to role model healthy eating, i am concerned that it may strain our relationship further... Thus being counterproductive to why we are trying to spend more time together. I know she is proud of me for my weight loss but i know it is killing her that she has given up on herself... She was always the one that COULD loose the weight when i would stay consistently overweight. I want to help boost her up, not have my healthy choices make her feel worse. To avoid the food thing I thought of ideas like going to see christmas lights at this place called Longwood Gardens, getting our nails done, but i know it will somehow end up revolving around food... Anyone have any suggestions, tips or HELP they could offer as far as ids of things to do or how i may approach this topic in a tactful and sensitive manner... Im open to hearing anything.