I took DS swimming at that age, when he got a bit overweight. We started by just doing a length of the pool then messing around. Next week, 2 lengths. Week after that, 3. Within 6 months he could swim a mile. We set ourselves small milestones along the way: 100m, 200m, 250, half a kilometre, a kilometre etc and at each one he got a small treat which was non-food. I didn't mention it would be non-food, I was just trying to instil the idea that treats don't have to be food - so he'd get a comic or a mini Lego set or a new tee shirt.
We also regularly went for cycle rides - about 5-8km a couple of times a week.
We had a trampoline and we played silly games on it together, like popcorn (jumping over a football on the trampoline.) You only need to do that for 10 mins while the pasta is boiling.
We'd go to the playpark when it was quiet and I'd try to do things like swinging from the horizontal ladder bars (not sure what they are called) then get him to show me how to do it. Children's bodies - even slightly heavy ones, are better at this, so he could usually do a couple and then got proud of himself and did a few more.
I found an old pedometer which he loved using - it made him go from hating walks to loving them - amazed he had walked 2000 steps on a short walk around the park! These days, as a young adult, he loves walking around the city he works in and often does 20k steps a day - he still loves checking his step count.
Small, silly things like dancing in the kitchen or having a tickle-chase game etc can also help keep them active.
Never ever mention weight or size. Focus on strength and fitness and agility. Look for things she enjoys and can get good at, and try to add a bit of exercise into daily life. We used to go for a hill walk most weekends and chat about things that took the focus off the walk - stuff like what would he spend a million pounds on just for himself or just for other people. Or what would his dream home look like. We ended up walking far further if we had chats like that.