I think you're a very good friend for being so concerned about this girl. I pray we may all be as lucky to have as good a friend as you!
Unless she brings it up, don't talk too much about her weight problem. Like you said, she's insecure about it, and it will do no good to chat about it. Just help her do something about it. And since she now knows for sure that you want to help her, don't feel bad if you suggest healthier activities. You two want to go out to eat? Do some research and find some restaurants (Subway is a great start) that have more healthy menu options so you can offer those suggestions. Go for lots of walks (which, having broken my leg before, was very beneficial once I got my cast off in getting my leg muscles back to working order). Find other good activities--riding (obviously) is great exercise. Other ideas: Rock/wall climbing, bike riding, frisbee in the park, hiking, skating, etc. Turn your friendship into an active friendship, not a sit-around-watching-movies-eating-chips friendship. It will be a lot of fun for both of you too!