Thats some strong shit your on to be able to pull that spin off.
Furthermore, who appointed the health board in NYC? The Mayor, so why would people he gave jobs to vote against him?
Using your "rational" logic, why isnt bloomberg limiting more things? Fast food, no more double quarter pounders, no more large fry's, no beer over 16oz, no juice over 16oz.
Just where do you draw the line on your made up government powers?
Spin? Your position is just baffling to me. There is likely nothing that legally prevents Bloomberg from restricting other fast food portion sizes.
1.) Is it within the mayor of New York City's power (through health boards, etc) to implement regulations in order to improve public health? Yes.
2.) Is this a regulation intended to improve public health? Yes.
3.) Does this regulation infringe on powers retained by other legitimate governing bodies under the city charter or violate state or federal laws? Not that I am aware of.
4.) Does this regulation violate rights guaranteed under the US Constitution? Not by any court precedent that I've seen.
The only case I can see is if someone is able to establish that this particular restriction cannot hope to accomplish its objective of improving public health in any way, and that seems unlikely.
Therefore, why would it be illegal? You seem to want every regulation you disagree with to be somehow prohibited by the Constitution. There are many things in this world that would be perfectly legal, yet perfectly stupid to do. This is one of those.