That's good from your point of view. You want her to be healthy and go to the gym. How do you persuade her to go to the gym? Sometimes it is useless to preach blindly. We can try to infect her with our own actions. If we can take part in some fitness by ourselves first, and then constantly mention the benefits of fitness to her in daily life, so that she can see the effect of fitness from you, then she will gradually be willing to understand and may go with you.
Then, if possible, you can find some simple and interesting fitness exercises suitable for your girlfriend's current physical condition, or two people can exercise together, so that she can gradually adapt to fitness, and under your guidance, tell her what to do and correct her wrong actions. I'm sure she will be very willing. Because such interaction will also enhance the feelings between the two of you and get to know each other better.
But then again, everyone's hobbies are different. We can't force others to do things she doesn't like. Although my girlfriend is in poor health, she may get better through fitness, but she doesn't like it. We can think of other ways, such as supplementing some nutritious food or nutrients, to keep her body healthy with as little exercise as possible.
But anyway, your girlfriend met a good man.
I wish you well, too, so that your girlfriend's health can get better and your relationship can be sweeter.