Believe it or not, this is exactly what some propose. Read about it here: http://www.theatlantic.com/national/archive/2011/03/we-dont-need-more-stigma-for-overweight-kids/72321/
Here's what they have to say:
This idea--that we've gone soft in more ways than one--has come up again and again in Slate's effort to crowdsource a remedy for overweight children. "Schools should actively stigmatize being fat," writes one member of the Hive; "few things are more terrifying to a kid than being an outcast." Another declares, "We need to stop telling children to 'love themselves the way they are.'"This is ludicrous. The reality is that these kids just don't know better, and they're bombarded by a media telling them to eat junk food in large quantities.
If anyone is at fault, it's the parents.
Yes, I wrote that. I place the fault in the rise of child-hood obesity squarely at the feet of parents (although allowing the government to take custody is just plain wrong). I realize that parents are often as ignorant as children when it comes to nutrition, but they are parents and should educate themselves.
If you see your entire family getting fatter and fatter, then its your responsibility to learn what you need to do to change that course.
I also put fault on the government for not regulating food quality and allowing kids to be bombarded by advertisements for crap food. We banned cigarette advertisements, so why can't we ban advertisements for sugary drinks, cereals and snacks?
The government is also at fault for subsidizing junk food over healthy food, but that's a whole other rant.
But, to stigmatize kids for the faults of their parents and the government? Sorry, that I don't agree with.