The challenge to the large soda ban has less to do with substance, more to do with procedural issues. The plaintiffs argue that the the Board of Health, which voted to implement the ban, does not have the authority to do so. Rather, that authority sits with the New York City Council, the lawsuit argues. Here's a key paragraph from the lawsuit, in which the soda ban is described as an "executive fiat:"
Over the public objection of 17 members of the City Council, the legislative body elected by the people, the Board of Health has decided to tell the people of New York City how much of certain beverages they should drink. The City Council knows how to legislate; it has considered legislation on obesity and nutrition; and it has repeatedly rejected proposals to address those issues by targeting certain beverages.The Board of Health's decision nonetheless to ban certain sizes of sweetened beverages in certain outlets, imposed by executive fiat, usurps the role of the City Council, violating core principles of democratic government, and ignoring the rights of the people of New York City to make their own choices.
As the lawsuit points out, it likely would be a whole lot harder to move the soda ban through the City Council. Michael Grynbaum notes in the New York Times that some of its own members were circulating a petition urging the Board of Health not to put the new regulation in place. Some of Bloomberg's other, major public health initiatives - banning smoking in restaurants, for example - went through the City Council rather than the Board of Health.
New York City argues that the Board of Health does indeed have the authority to create a regulation that promotes healthier living, which is the whole point of having a board of health. “The Board of Health absolutely has the authority to regulate matters affecting health, and the obesity crisis killing nearly 6,000 New Yorkers a year — and impacting the lives of thousands more — unquestionably falls under its purview,” Bloomberg spokesman Marc La Vorgna wrote in a statement to the New York Times.