What are appropriate ways to support someone who is trying to lose weight? How can I encourage her in a healthy way?
Get her to do a little bit of exercise. I'm not talking about going to the gym unless that's your thing, but you can do very simple things, like having a walk together while chatting. Use your smartphone GPS, start low like a few miles, and make sure you got proper shoes. At first the goal is not to exercise, but to get her out of the "I can't exercise because it's too hard" mindset (if that is indeed the case, maybe she's already exercising).
Anyway, try to convince her that a little afterwork walk is a relaxing way to end a stressful day, aim for 30-60 minutes of gentle exercise. That burns little calories, you gotta be careful about what you eat afterward because it'll make you hungry, but it works. Once she's a little bit fitter, you can suggest other, more intense activities, but it is important to start low so she's not discouraged.
I did somethink like that a while ago with a buddy: we got shredded by drinking beer every day after work. The trick is that we had to have the beer in a bar which was 10km away, and get there using our bicycles... then when it got too easy we picked a bar further away. The record was 160km roundtrip, but you really gotta do that on weekend, because it does take a while!
As for food, it's simple: no processed sugars, no junk food, medium amount of fat, veggies, and sort the rest by glycemic index, make sure you cook and not buy processed junk, and make it tasty.
If you both get hungry and crave for a snack in the middle of the afternoon, I've found adding lentils to the menu at midday to be quite excellent. You can cook them in many ways (like curry etc), they taste quite good, and they're a really slow burning fuel (low glycemic index).
I was looking for food that was easy to carry in a backpack and would get me on top of the mountain nearby without getting too hungry on the way, so I tried various combinations, and found out that stuff like lentils, peas, whole grain rice, basically everything that has carbs but low glycemic index provides energy for a really long time without craving for a snack...
This worked on my dad too. He has a little bit of diabetes. His breakfast was white bread slices dipped in tea, so by 11AM he was in hypoglycemia and binging on junk food. Fix was to reduce the bread and switch to brown bread, and add like 50 grams of lentils or baked beans to the breakfast, maybe an egg or a bit of fat like a sausage... no more hypoglycemia!