I don't know if this is type-related, but I can relate to her struggle A LOT since I have battled my weight all my life and only recently underwent a complete change and lost a lot of it (and I am by no means thin yet). So I will just share my experience.
I wanted to primarily be more fit and healthier, but I needed a concrete goal. I decided I will run a specific half marathon a year down the road and started training for it (not by running right away, but by swimming and the elliptical machine to take stress off my knees). Another goal was to look good in a dress for a special occasion and I keep visualizing both as a motivator. I would literally spend an hour on the elliptical imagining myself crossing the finish line or for the first time in my life wearing a bikini (maybe shallow, but if you have never felt comfortable enough to enjoy a day on the beach in even a one-piece bathing suit, the prospect of wearing a bikini is huge). As another strategy, I cut out all room for excuses or lapses (no junky food ever, ridiculously healthy diet, workouts every day without fail). I think I simplified the whole process by removing all potential for not sticking to it (*one piece of chocolate will not hurt* - it will for me). But really, it was my fitness goal that did the trick (and watching the muscular changes in my body). I turned into a total narcissist and paid very close attention to how my body shape was changing and muscles were becoming visible. I also did yoga every day, which is amazing for toning and easy on the joints. Yoga builds muscle (people have the wrong idea about yoga) quite effectively.
I think even if her swimming is leisurely, making it a more routine and more frequent habit can make a difference. Five days a week and perhaps setting a goal of swimming a certain distance in a certain time. It does not have to be hardcore racing to be effective. She will burn calories even at a leisurely pace. Walking might be another option (with the fitness gadgets that people mentioned).
Most importantly, let her know that you will love her regardless. I have had partners who wanted me thinner and praised me for losing weight. It always backfired because eventually I felt too awful about my body to really want to be good to it. So if she were me, I would like support in eating healthy foods together, being active together, noticing changes in a way that does not turn into fat shaming, and feeling accepted regardless and ideally have someone
worship (haha) my body the way it is (since the changes are changes I want for me). Do yoga together. I can send you links to some yoga routines that will make anyone work up a sweat and make muscles burn.
And I feel for her. It's hard.
About how much would she like to lose?