Others spoke forcefully of the need for action to deal with an obesity crisis.
"I feel to not act would really be criminal," said board member Susan Klitzman, director of the Urban Public Health Program at Hunter College. City Health Commissioner Dr. Thomas Farley called the rule "a historic step to address a major health problem of our time."
The restaurant and beverage industries complained that the city is exaggerating the role sugary beverages have played in making Americans fat.
"This is a political solution and not a health solution," said Eliot Hoff, a spokesman for an industry-sponsored group called New Yorkers for Beverage Choices, which claims to have gathered more than 250,000 signatures on petitions against the plan.
He said the group is considering suing to block the rule.
"We will continue to voice our opposition to this ban and fight for the right of New Yorkers to make their own choices. And we will stand with the business owners who will be hurt by these arbitrary limitations," Hoff said in a statement.
Enforcement will be carried out by New York City's restaurant inspectors. Violations will carry a $200 fine.
Complying might prove complicated for some establishments.
Starbucks is trying to figure out whether the regulations bar it from selling its calorie-packed Frappuccinos in the 24-ounce size.
Another issue could be iced coffee, which many cafes sweeten with liquefied sugar. Customers might have to add the sweetener themselves.
Fast-food restaurants with self-serve soda fountains will be prohibited from giving out cups larger than 16 ounces, but people will still be allowed refills.
Manhattan pizza shop owner Vinnie Siena said halting sales of large sodas will hurt his already thin profit margin, unless he raises prices.
"I'm having a tough time as it is. They don't want the little guy to survive, it seems," he said.