I would definitely support her on this, and encourage her to discuss with her doctor beforehand.
They are much better than SW, WW etc IME. I was using Saxenda from January and now I use Wegovy. I have not been a super responder, and I am losing slowly. My endocrinologist is very happy (she says it is better than losing quickly, for my body and for lose skin). This enables my body to reset its set weight and balance my metabolism again. With regards to the health concerns, I discussed it with my doctor, a dietician and an endocrinologist (who now follows me) for 6 months before I started this treatment. The health risks of being obese far outweigh the possible risks of these injections, and we are tackling the issues now so that when I do come off the medication, I have a good idea about nutrition, how to maintain etc etc.
The common misconception is that people expect this injection to make the fat simply disappear easily and quickly. I see a lot of people posting on social media 'I've only lost 1 lb this week. I am paying good money and expect more!' 🤦♀️
It doesn't do this! You still have to do all the hard work. You have to balance your diet, learn what's what. You have to work hard at it.
With meal replacements, WW, SW ETC you are not learning, you are mostly replacing food with fake food stuffs.
UPF is the villain that needs to be tackled here, IMO. I would encourage you and your DD to read Ultra Processed People and The Glucose goddess. The obesity code and why we eat too much are other great informative reads. You can also listen to them on audible, I believe. Cook real food. Once she has learnt about this, she can change her eating habits and then look at starting the injections.
Taking the injections and not making any great changes to her lifestyle won't help her in the long run and she will just put the weight back on when she stops. But they are brilliant at helping you maintain newly implemented habits. I had a terrible Coke Zero addiction. I haven't touched a drop in over a year now. I also gave up alcohol very easily and now will happily have a glass, on special occasions, but no more. My blood sugar was all over the place and I shook a lot. Gone. This didn't happen with WW or SW as they were still encouraging me to have a bar or a meal replacement, none of which is real food. (Which I why I wouldn't encourage her to do these plans. They are BS and create bad habits/yo-yo dieting.) As an ex smoker, I know that I will always be saying no to these things, but that's all down to mental strength. But they did help a lot in breaking the habit!
I understand her anxiety about exercise. I feel the same. But only now that I have lost some weight am I willing to start exercising. Slowly slowly. But I know that losing weight doesn't equal healthy and I have made myself targets and goals to aim for.
Shred the weight first, and then tackle the health and exercise, because they are too different things altogether.
Finally, don't shut the conversation down. She is 19 and an adult, but she is also only 19 and she has come to you to discuss it. Also, please do not buy cheaper versions. These are unregulated and potentially very dangerous!
There is an injectables board, where you will get more information from people using the medication rather than people whose neighbours cousin met someone in a supermarket whose head caved in due to these injections etc etc.