Wrong way to tell someone this?

Sometimes you just have to be 100% honest! I had to do the same with my sister!

Today I told my little sister that her eating habits were concerning me and asked her if she was eating out of boredom or depression. This completely set her off and caused us to fight. I explained to her that I wasn't trying to be mean, that I was concerned that if she kept up her eating habits, she would have major health problems and that she stays in a bad mood lately, probably because of how she eats.
She has 6 pieces of toast & 2 bowls of cereal (immediately following the toast) - no joke. She eats a double cheeseburger at least 3 times a week. I really don't want her to become morbidly obese and have so many problems that she nearly dies.
Was there a better way of telling her this?

So you called her possibly depressed or bored or fat. Then told her she would be doomed with health problems and that she's a snatch because she eats like crap.

Yeah. I'm not sure why that set her off. No clue at all.

I think its great that you openly asked her about her health and showed concern. I think the fact that she reacted so dramatically shows that you are, in part, on the right track. People often become defensive when trying to hide something like depression. But put yourself in her position, how would you have reacted if she said the same to you?

Since she's family, I think you can pretty much say anything you feel needs to be said.. but maybe you need to take a different approach and offer to help her out by sharing new (healthier) recipes with her or asking if she wants to exercise with you (by asking her to go on a walk, hike, etc... don't ask her if she wants to go to the gym or she'll probably go off again).

Personally, I think it depends on how old she is. Is she 8? 18? 28? Depending on her age she is likely to be fully aware that she is eating out of boredom, depression, and that this could be and may cause health problems. More info would be helpful before at least I can give a proper opinion

Very few (if any) people like to be preached to. She's your sister, and you love her. So I understand why you wanted to say something. However, there is really no right way to tell someone who hasn't asked for advice how you think that person should change her or his life. However much you care, unless you are her guardian, it's not your place to tell her what to do for her health. Telling someone who doesn't want to change can often have negative effects, the person may do exactly what you didn't want to "show you who's boss".

As has been said many times, you can't change someone who doesn't want to change. You can set a good example. You can support her and make healthy choices easier. For instance, you can invite her to eat with you or exercise with you. You can say what you're doing for your health and mention how it makes you feel better in ways you wouldn't have expected. On rare occasions (like once a decade) you can say something like, I worry about whether you're getting enough nutrition. And if she doesn't respond, drop it. If she wants, she can follow-up, then you can make suggestions.

Alright, well you still haven't said how old she is, but the person above (officerfuzzy) has some great advice.
Instead of making it food orientated, find out what could be causing her poor relationship with food but without mentioning her eating habits... eg. if there's something wrong with you and it's causing you to express the problem through other habits, instead of talking about the outlet for the problem, get to the root of the problem itself. I'm probably not making that much sense as i'm absolutely knackered but i'm sure you get the gist of it haha.