Has your company hosted a competition like this?  Any suggestions on how it was handled?

Frankly, I would be afraid to do this. I know participation would be voluntary, but it seems fraught with possibilities for problems--discrimination, harassment, etc.--and HR headaches. 

Maybe your healthcare provider has some kind of program like this that you can use that has been reviewed by an employment attorney.

I've heard of a company where the people who would like to participate put X amount of money in the pot.  Whoever loses 10% or more of their starting weight wins.  If there is more than one winner, then they split the pot evenly amongst all winners.