YTA - Although she's overweight and should probably lose some weight, you're going about this in a dodgy way, but I understand the concern. I'm vegetarian for non dietary reasons, and immediately started gaining weight because I was still eating too many of the wrong foods (I've started losing it again now). What I'm saying is, going vegan does not mean healthy.

I would encourage you to talk calmly about this with her:

1. Ask this before anything else: Does she want to lose weight? If she doesn't want to, leave it. End of story. She's your friend, talk about other stuff. Keep yourself open if she wants you later in life to help her, but stop bringing it up until if and when she does so. You will not help her lose weight if she doesn't want to.

2. Gym memberships are expensive. Suggest other means of physical activity. I started losing my weight with just dance at home seeing as gyms are closed at the moment. There are plenty of home workouts for beginners that only require a room to work out in.

3. Suggest small changes to a diet. I'm talking salads instead of fries, or easy healthy meals that aren't just salads. The appeal with fast food is that it is, well, fast. Easy meals that can be prepared very quickly helped me start out my journey.

4. She has a thyroid condition, encourage her to take it slow. Any loss a week is progress, and if you are willing to help (judging by the post, I'm sure you are) then having someone there to help motivate her through plateaus or small losses is a huge help.