I think it is only logical that as a husband you are concerned for her health. But it is her life and she has to be the one to make the changes and even more so want to make them.
My husband is over weight and crazy unhealthy, so I do understand where you are coming from.
But part of me reads your post and thinks you may be coming across a bit pushy and perhaps that is why she is cranky all the time lol.
I was talking with my sister not that long ago about dieting and how people around us can show support. No one is so stupid that they don't realize their food is making them fat. We may try to live in denial or ignore it but we know. And it can be very difficult to walk that line of support without being judgmental, pushy, or even worse make us feel unattractive or worse about ourselves then we already do.
I think the best type of support is just being there for the person. Letting them know that you are there for them & will support them at their pace.
I would for sure talk to her about seeing a new doctor and/or a endocrinologist. I have PCOS myself it sucks lol. Maybe even seeing a nutritionist?
Maybe tell her about this website and ask her if she would like to join. Did you tell her you were posting here? I just find it strange I guess because it seems like you are talking to her about the issue but is she just not doing anything herself? Again you can't force someone else to change and trying will just lead to resentment and alot of bad feelings. Sometimes it can take years before someone is ready to make that change.
Instead of focusing on her losing weight maybe talk about eating healthier. Does she do all the shopping and cooking? You can try shopping together, I always go shopping with my husband I like that
Maybe offer to cook more meals or cook together. Take a cooking class together and look up recipes and make them together. Which is super romantic too. It doesn't have to be about losing weight but instead eating healthier meals and trying new healthier foods.
When i cook for my husband I add in tons of veggies and new stuff that he would never eat on his own. He has really loved some things that he never thought he would and has been introduced to new foods and lots of veggies. the other week I made vegan brownies packed with zucchini and pumpkin and dark chocolate. He loved them!
Offer to take a walk in the evening after dinner together. Plan fun romantic dates that involve activity like going to the zoo and walking around or to the park where you can walk and pack healthy lunch. Go swimming, etc... Kindof sucks that it is winter though idk where you live. Maybe take a dance class together?
Small changes like switching to whole wheat and adding in veggies and fruits with meals can add up to bigger changes.