Of course he thinks they do. That's why we have constitutions -- so they can be changed in tumultuous times. As Bloomberg sees it, the first obligation of government is to keep your "children safe." How this wide-ranging duty affects other societal concerns -- liberty, cost, etc. -- is largely irrelevant because ... well, because toddlers are cute. Those tobacco-addicted Founding Fathers didn't have the decency to include a single line about keeping Americans salubrious or children.
Bloomberg is an authoritarian. He's not an authoritarian in the way Josef Stalin or Pol Pot was authoritarian, but every instinct tells you he's a man who would use any power given to him to govern every aspect of public and private life whenever necessary -- or, more precisely, whenever he finds it necessary, which is frequently. All said, he's exactly the type of person who makes the Constitution a necessity.
Anyone who believes your caloric intake is government's prime concern should be watched carefully, of course; but no matter what crusade the man's on, his rationalization for limiting personal freedom is a dangerous one. Some of his proposals are popular (smoking bans), and others are less so (limiting portion sizes and banning ingredients), but all of them set precedents that distort the relationship between government and citizens. The jump from minor infringements on personal liberty to giant ones is a shorter one than you think. Allow a politician to tell you what your portion sizes should be and the next thing you know you're letting Washington force you to buy insurance you don't want.
If the Bloomberg administration believes that salt -- "the greatest public health threat facing" New York City -- is worth losing your freedom over, imagine what he'd have planned after a terrorist attack.