I was in a similar situation to your DD as a teenager, in that I was tall and a bit overweight, but held it pretty well, and my mum (who is a great mother in many other ways) was not helpful. She is pretty slim and petite and often commented on my weight, told me off if I ate a cake or something (even if she and everyone else was eating the same thing!), while also cooking a lot of processed convenience foods. I know she meant well but it reflected her own issues with appearance and insecurity.
It is good to see that you're coming from a much different perspective than my mum, and so I've no doubt you will help your DD get to a healthier position. From my experience, I'd recommend not worrying too much about losing the weight right now. Instead, I think it is much more important that you take steps to help her develop a good relationship with both food and her own body - the rest will follow later.
While her weight is very worrying for her tender age, she is "only" overweight now - the real danger when you carry it well is that it can continue to creep into adult obesity without really even realising it (this is has happened to me in the past). So take it in small steps. The most important thing to focus on at the moment is to start to change behaviours so this upward trend stops and then starts to slowly reverse over time ( the longer term "cure"), rather than focusing all your energy on changing her weight now (a "symptom" of a deeper problem).
As part of this, I'd kindly suggest spending some time giving cooking and basic nutrition lessons to all your DCs (so your DD doesn't feel singled out, also it is great for everyone to learn how to cook regardless). You could say it is to prep them all before they fly the nest for uni etc in a few years' time. If your DD is able to make a decent meal, she might be more inclined to eat it - if she's not eating decent meals, she will definitely be grabbing for crappy, unhealthy snacks to fill the gap. And if she enjoys the process, she will be more inclined to experiment with healthier foods, like different vegetables.
Try and also get some activity in with your DD, suggest going for a walk together everyday or something similar. Doesn't have to be heavy or daunting exercise - try to see it as more for mental health, rather than just about weight. Sitting around inside all day, playing computer games, is not good for the mind and is also going to make her snack out of both boredom and comfort.
I'm now healthy and happy at 33 years old, after years of yo-yoing between the normal, overweight, and obese categories. But, after many years of having a more extreme love/hate relationship with food, the benefits of a better, more balanced relationship with food and my own body image goes far beyond weight, it makes me a healthier and more positive person. But it is a long haul and goes far deeper than just a number on a scale.
Hope this helps - good luck 