You don't have to feel guilty.
If it comes to weight loss no one is in charge except you (well her...) self.
If you can invite her over, don't talk about the topic until she wants to and if she wants to go on a trip say you can't because you are on a diet, but not more.
If she wants to talk to you about it (she might even just want tips) she will come to you.
Other than that I guess you might both like to see each other, so why not? I guess you gals had more in common and have more to talk about than just this one thing