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The obesity rate for African-Americans in New York City is higher than the city average, and city health department officials say minority neighborhoods would be among the key beneficiaries of a rule that would limit the sale of super-size, calorie-laden beverages.

But the N.A.A.C.P. has close ties to big soft-drink companies, particularly Coca-Cola, whose longtime Atlanta law firm, King & Spalding, wrote the amicus brief filed by the civil rights group in support of a lawsuit aimed at blocking Mr. Bloomberg's soda rules, which are set to take effect in March.

Coca-Cola has also donated tens of thousands of dollars to a health education program, Project HELP, developed by the National Association for the Advancement of Colored People. The amicus brief describes that program, but not the financial contributions of the beverage company. The brief was filed jointly with another organization, the Hispanic Federation, whose former president, Lillian Rodríguez López, recently took a job at Coca-Cola.

The N.A.A.C.P.'s New York office referred questions to the American Beverage Association, the soft-drink industry's lobbying group and the primary plaintiff in the suit against the city's new soda rules. The association referred questions to Coca-Cola, which did not immediately respond.

At the hearing on Wednesday in State Supreme Court in Manhattan, lawyers for the beverage industry argued that the Board of Health had overreached its authority by unilaterally ratifying the new rules. The city rejected that argument, saying the restrictions were well within the board's purview to regulate public health matters.

The hearing ended with no immediate ruling; Justice Milton A. Tingling Jr., who presided, adjourned without comment. The beverage industry said it was requesting a stay of the soda restrictions while the case was being resolved.

While the industry has successfully fended off higher soda taxes and restrictions across the country, it has been increasingly under siege from public health officials concerned about the adverse effects of sugary drinks.

New York unveiled its soda plan in May, and other states and cities have since pursued similar measures. On Wednesday, Gov. Deval L. Patrick of Massachusetts proposed that soda no longer be exempt from the state's sales tax; lawmakers in Hawaii and Nebraska have also recently proposed higher taxes on sales of sugary drinks.

In its amicus brief, the N.A.A.C.P. acknowledged that obesity was a significant problem among blacks and Hispanics. But the group urged the city to create a more holistic program to attack the problem, including an increase in financing for physical education programs in public schools.

Mr. Bloomberg's plan, the brief argued, would disproportionately hurt minority-owned small businesses, which faced competition from larger convenience stores like 7-Eleven that would be exempt from the soda restrictions because of a quirk in New York's regulatory structure.

"At its worst, the ban arbitrarily discriminates against citizens and small-business owners in African-American and Hispanic communities," the brief said.

The plan has also been ardently opposed by several members of the City Council's Black, Latino and Asian Caucus.

The city's health commissioner, Dr. Thomas A. Farley, said Wednesday that he was "disappointed" the N.A.A.C.P. had opposed the plan. "African-Americans are suffering disproportionately in this crisis, and I don't think the N.A.A.C.P. should be siding with the big soda companies," he said. "They are attacking public health officials who are trying to respond to that crisis."

According to the health department, about 70 percent of black New Yorkers and 66 percent of Hispanic New Yorkers are obese or overweight, compared with 52 percent of white non-Hispanic residents, based on a 2011 survey.