I had anorexia, starting when I was 12 or 13. I have heard that it often affects girls (in particular) who are intelligent, perfectionists, sensitive, hard workers and self-driven. That was certainly true of me. Mine started because of a cutting, unkind comment made by someone, being jilted by a boyfriend (yes, even - perhaps especially - at that age), and being unhappy with who I was. However, I took some pride in being able to manage my eating in order to lose weight - to prove that I could do it. The problem was that this got out of hand and by the time you are at this stage it is too late - you are not the person you once were and you cannot suddenly start eating again. I don't really know what would have helped me - I was at boarding school so I suspect a home life might have helped. It's important to feel respected and loved and for someone to be interested in you. One of the things that makes matters worse is that often you are seen as 'difficult' or 'a problem'. In fact, I remember to this day a teacher walking into the school sanitorium and saying 'How's the problem girl today?' - as I hid away a doughnut that I had to pretend I'd eaten.
I think another thing that may help is for an adult to admit to imperfections in their own lives - it's easy when you are young to think that everyone in your family except you has been successful and is somehow a better person than you are. That you are somehow not up to scratch. It's important to learn that this isn't true. How did I recover? Well I did avoid hospitalisation (although was down to 6 stone, from 12!) but I home-schooled for a while, I had quality time with my parents (very important to me) and, perhaps most importantly in my case, I was given a puppy. The latter helped because I suddenly had another life that I had to look after. A life was dependent on me and I was able to move my thinking outside of myself. That puppy also loved me unconditionally, without any expectations or recriminations. This wouldn't be possible for everyone, and it might not work for all but I mention it because I see it as an important part of my own recovery. Things that I think made things worse? Doctors and nurses treating me like a problem; the drugs that had awful side-effects (I remember hearing voices!); the feeling of inadequacy. Things that made things better? Individual attention; being taken out to tea (bizarrely!); walks in beautiful places; watching the sun rise; owning a puppy. It took a few years . . . I think once you come out at the other end, assuming you are one of the lucky ones who do, then you are a stronger, more compassionate person for it. I have had no recurrence and I have learnt to be happy in the moment (call it a Buddhist philosophy or Mindfulness!).
I have written all this down in the hope that it may help others. What would I recommend a grandmother to do? Well, with the agreement of the parents, I would just make sure that you show how much you love and admire your granddaughter; talk about some of the failings in your own life - perhaps a boyfriend who jilted you (easier for a grandparent to talk about than a parent!) or a time when you felt that you failed parental expectations; take her for treats - go out for a tea or a coffee (of her choice) or a shopping expedition or a walk; ask her to join you on a yoga weekend or evening; be an ally, a friend; build trust but never, ever betray that trust by talking about her behind her back, other than fighting her corner.
I don't have the answers and wish I did. Anorexia is an awful illness, needs very careful handling and is not the fault of the person who is going through it - or of those around them. Having said that - and this I know is a very sensitive area - I think that parents (particularly academic or high powered ones) can be a little distant. Fathers, perhaps in particular, don't have time to give individual attention and sometimes even if they did, wouldn't know what to do with it or how to build a close one on one relationship with their daughter. This isn't an easy thing to say and is certainly not an easy thing to put right. If this is you, ask yourself, could you say out loud 'We love you so much; you are so precious to us and we want you to be the person you want to be and we'll do everything we can to make that possible.' Could you hug and hold your daughter or granddaughter? This will come naturally to some parents but not to others. It certainly doesn't mean that they don't love just as much or as deeply but it may present a challenge to others to recognise that, so may, in these circumstances, need working on.
I hope this helps.