I'd probably take the "fatness" out of the equation and like you say, concentrate on wanting her to be/feel healthy.

If she's complaining that she's tired then explain that she'll feel so much better if she does a little bit of exercise - both mentally and physically.

So concentrate on the things SHE'S complaining about and suggest ways that she can feel better, rather than concentrating on the fact that she'll LOOK better if she avoids the junk and does exercise.

Hope that makes sense.

I'm sure she's not stupid and will work out that you think she's putting weight on but you might get better results if you give her the impression that it's not whether she's fat or thin that concerns you just that she's fit and healthy and can enjoy time with Jazz - especially when she gets to the stage where she wants to run around the park.