She sounds very similar to me at that age, OP.
I put on weight at puberty and yo-yo dieted in my teens (doing crap, unhealthy things like Slim Fast and living off watery cup-a-soups though). At 18 / 19 I just started having fun with my mates, which meant drinking and going for curries at weekends, as well as many a late-night kebab. I was very happy, but I also got fat.
I would have been a bit crushed if my mother had brought it up, but I wouldn't have been offended. I knew it wasn't great that I was getting fatter, but I was having such a fun time I didn't care much.
However, if I'd tackled it then and learned what a healthy diet looked like, I might not be where I am now - 20 years later and only just getting back to a healthy weight.
The junk food is the problem -- it's bad for so many reasons.
Does she like to read? I recommend Why We Eat (Too Much) by Dr Andrew Jenkinson. It's not a diet book per se, it's about how our metabolisms work, why obesity happens and why processed food is so particularly bad. Maybe she just needs a nudge in the right direction and a bit more knowledge, so that she can get in control of her eating.
Perhaps one approach you could take is to buy the book for yourself and just make conversation about it, rather than making it all about her and her weight? My husband read it after I kept talking about it, and now he's a convert.