That's a tough situation. You want to encourage healthy eating and behavior, but one of the things to avoid with a perfectionistic child is modeling perfectionism. I think you're taking a good tack by stressing that you want to be healthy. Perhaps you could model setting realistic goals, a realization that perfection may be unattainable, etc.: communicate that everyone's bodies are different, that you just want to reach a certain weight goal without making it your full-time hobby, that doing a few things can help you be a lot healthier, etc. Also, in this particular case I'd stress that being too thin can be AND LOOK very unhealthy, and that the trick is a good balance rather than restriction.
We have this problem too, but with our son. I think that he's got a good dose of parent fatness shame mixed in with his perfectionism. I threatened to force-feed him a suet cake one day if he didn't can it with the talk about his needing to avoid getting fat (he's also a bit underweight for his age). That behavior's luckily been on the wane lately (two cakes later... j/k), and he's also been eating more meat.
Here's a
past thread on perfectionism. A lot of the techniques for academically-related perfectionism are tough to relate to your situation, unfortunately.
