Well, it really and truly is a difficult issue you're addressing. Weight is almost universally at the core of how people view their own attractiveness. For some people losing weight is a genuinely difficult task, it's easy for people like me and you (I'm assuming) to talk about staying fit, because we already are fit. But for people who aren't, it's really difficult.
One of the basic conventions of our society is that when people have a flaw, even if it is clearly visible, we don't point it out to them. It's not polite to tell stupid people that they're stupid, ugly people that they're ugly, or fat people that they're fat. So it's understandable that your girlfriend doesn't want to be impolite to her friend by suggesting she take up a weight loss program. Because losing weight can be so difficult it's a seriously personal issue for some people. Very very (very) close friends can openly talk with each other about the other's flaws, but if your girlfriend isn't that close of friends with this girl, then trying to talk her into losing weight is only going to embarass this girl, causing her to get angry with your girlfriend, and upsetting the balance of their group of friends. If worst comes to worst the ultimate result (instead of this girl losing weight) could be that this girl feels so embarassed about having been approached that she stops hanging out with the friends who approached her, ultimately losing social ties, and possibly (as many people do) eating more do deal with the emotional trauma. So yes, approaching this girl could help her, but it could also make things a lot worse. As a general rule, when it comes to something as personal as weight, it's best not to approach someone about making changes, and just hope they decide to work on it for themselves (and if they do, and are open about it, then you can offer to help them).