> There are valid counterarguments to the overweight values, a lot of women who might be overweight are healthy because different % of fat are acceptable depending on the structure of the body

But the BMI takes into account the mass, not the size. Usually women have less lean muscle mass than men, which would mean that for a given size and weight, they'd have more fat, without influencing the BMI. I also think there's quite some leeway. My BMI is "normal" at 24, and I have a fair bit of belly fat.

Very athletic people also don't fit in the BMI tables, a dude like Schwarzenegger is probably well in the overweight category if not above because of all that lean muscle, but is also probably healthier than average. These people are extreme outliers, though. I don't think they're anywhere near 1% of the population, so you can't really argue they skew the numbers.

> As for offering them that is a nice thing, but I am curious about the mechanics (mutuelles) and such of the medicine.

It's apparently paid by the social security, but doctors are only to prescribe this when other means of controlling the weight have failed, such as adjusting nutrition.