"She is already pretty chubby and eats mostly whatever she wants, which will most likely lead to some more extra weight without my interference."
Here's your answer.
If she's already on this track, I think the best thing you can do is just love her, make her feel safe and comfortable, and let Mother Nature run its course. Eventually, she'll hit a point where that weight piles on faster and faster, and it becomes more and more difficult to take it off. If you make her feel beautiful and loved, she'll have no real motivation to lose the weight, and you can just sit back and enjoy as she becomes softer, fatter, and sexier.
There are (relatively) healthy ways to gain weight without putting oneself at a massive risk of disease/death. Slow gaining over a longer period of time is safer than rapid gains, as the body has more time to adjust to the added weight. Avoiding heavily-processed foods and restricting sugar intake helps too. (Much of the damage that junk food does to the body comes from processed chemicals, artificial additives, and artificial sugars). She can get a surprising amount of calories from all-natural butters, creams, oils, etc. She could also use weight-gain formulas. These are like protein powders, except that they add calories to your diet instead of protein. Her diet should include fresh vegetables and fruits as well as the heavier, more fattening foods. That way, she still gets the nutrients her body needs while getting lots of fattening calories too.
That's just a start. My point is that it's possible to eat a heavy, calorie-rich diet and gain weight without eating junk food 24/7.
Of course, there comes a point at which a woman is simply too big to avoid weight-related health risks, so keep that in mind. But hey, maybe your gf doesn't care --- in that case, I would just let her keep growing.