I have an eating disorder, so my view may be slightly different, but I have had it for over 10 years now, am in recovery (finally working) and every one close to be in aware. I wanted to let you know those details so that as it has a bais on my opinion.
If this were me I'd be very, very angry & extremly defensive. Eating disorders are a private disease and there is so much secrecy and shame involved, I'd probably have lashed out and said some very horrible things and cut the person off for a bit had I been confronted in this manner back before it were all out in the open.
That said it would also be a massive relief. It is a horrible secret to carry and incredibly isolating. For years I felt as if I have been watching the world but not been part of it. Also, had I had any intervention early on in my eating disorder I'd have possibly begun fighting in therapy quicker or been more receptive to treatment.
I think that the suggestion of trying to make her confess in a food related situation, while written with the best intentions, is very misguided. People with eating disorders are amazing at hiding them, especially if purging behaviors are involved & I think you'd find you were watching her every mouthful, which she'd be hyper-aware off - and I think it'd create a lot of stress and upset on both your parts.
I'd suggest firstly that you look into eating disorders, the facts, the symptoms, the treatments - it sounds like purging type anorexia to me, but also look at EDNOS and Bulimia. www.something-fishy.org/
this way if you do decide to confront your dsis you have reliable information behind you. There are many good books available for the loved ones of eating disorder sufferers and feel free to pm me if you are interested in some titles. (or if you think i'd be able to help in any way at all)
I think i'd go for confrontation, but admit you read the notebook, and explain what concerns led you to doing so. Expect anger, denial, and her possibly not talking to you for some while.
Another option could be leaving her with some eating disorder information, she will have likely read it all already (people with eating disorders are often in denial but also very well versed on the topic, part of the warped thinking - i still refuse to use the word 'anorexic' in reference to myself but could cite you so many articles and medical papers on the subject). This way she will know that you have your suspicions but it leaves the control to her - if she wants to talk she can, if not she can ignore it. But do be prepared for denial. I know this option would create a lot of anxiety for you, and I think in any case i'd own up to reading her notebook...trust is a huge issue for everyone, but more so in people with ed's, so let her trust you by telling her you broke it ifywim. (for the record I do understand why you may have snooped)
Lastly. She will need professional help if she is far into this. and even people with the thinking trait that do not have any full blown eating disorder still benfit hugely from treatment, it is so difficult to fight alone...but she won't get help until she is ready. I think this is the hardest part for loved one's to deal with. My DP & parents have seen me through 5 serious relapses, countless hospitalizations and lots of broken promises to 'be better'. I am now coming out the other end (i hope) and am mainly on MN as am thinking about TTC after a miscarriage caused by my eating disorder.
I wish you luck with this & am thinking of your Dsis too.
(sorry for horrible spelling & grammar, need to be doing other things but couldn't not answer your post)