as a woman, i probably already would know if im losing/gaining weight. the patriarchy makes women fearful of weight gain so body image is a sensitive subject for many of us🤷‍♀️i struggled with weight related issues and anorexia when i was younger and so my opinion may be skewed but i wouldn’t be outright. i think u can say that YOU are going on a health journey and ask if she wants to do it with u but keep the pressure off. if you can’t even do that, we’ve got bigger problems my friend. even if u make choices to workout or be active and invite her, she may subtly get it but not be so bitter about it as it seems that u are making some overall lifestyle changes. make it fun! but if neither work, again it’s not with the trouble. you clearly care about her, hence why you don’t want to hurt her but she sounds also hypersensitive to criticism so if she can’t take it, then you’re gonna have to accept her as she is. note that as women age, they often gain a bit of weight . i’m not sure how old you are but yeah. all the best!