Not all weight is fat. If you are 1.90m tall man and naturally big, you can easily weight twice as much than a 1.55 woman even if you are fit. How are you going to account for natural weight vs being overweight. Even BMI is very crude.
The weighing could be done at the end of the flight.
It's possible some people will actually get healthier. However, it's also much easier to lose 10lbs from dehydration and pooping than from losing fat (from my experience).