New York (CNN) -- New York City's attempt to keep people from fattening up on sugary soft drinks, by banning some of them, would disproportionately hurt small, minority-owned businesses, according to the NAACP and the Hispanic Federation.
The two groups have filed a joint brief supporting a lawsuit by the American Beverage Association in which they say New York's unelected Board of Health overstepped its power in approving the ban the sale of sugary drinks bigger than 16 ounces in certain city venues.
Due to take effect in March, the ban is meant to combat obesity and encourage residents to live healthier lifestyles, according to the New York Mayor Michael Bloomberg's office. But many have decried the ban as a sign of the growing "nanny-state" and an unfair intrusion on personal freedom.
It was passed in September by the New York City Board of Health, following weeks of intense debate.
In their jointly-filed amicus brief, the NAACP New York State Conference and the Hispanic Federation repeatedly claim that small, minority-owned businesses will suffer from the ban while their much-larger competitors will get a pass.
The ban will "selectively and unfairly harm small and minority-owned businesses by discriminatorily preventing them from selling large 'sugary beverages' while allowing their large competitors such as 7-11 and grocery stores to carry the banned sugary beverages," according to the brief.
7-Eleven -- manufacturer of perhaps the most iconic oversized drink vessel, the Big Gulp -- and other grocery stores and convenience stores will indeed be exempt from the ban, because they are regulated by the state, not the city.
The uneven implementation of the ban will harm the very businesses that can least afford it, said Hispanic Federation spokesman Jose Davila
"Any little thing is going to hurt them ... they're just subsisting," he said.
The mayor's office reiterated its commitment to the ban on Wednesday, citing the prevalence of obesity among minorities as one of the very reasons why the ban is needed.
"The obesity crisis impacting the nation, and disproportionately affecting minorities, calls for bold action and we are confident support will grow as more people learn about the unique impact sugary drinks have on this epidemic," said Samantha Levine, a spokeswoman for Mayor Bloomberg.
Coca-Cola has also donated thousands of dollars to an NAACP health education program called Project HELP, which included $75,000 over the past two years. The Hispanic Federation received an equal amount from the beverage giant in 2012, according to Jose Calderon, the group's president.
"If this was the first time that Coca-Cola had given us money, sure it would raise questions," said Hazel Dukes, president of the NAACP's New York chapter. "But it's not the first time ... Coca-Cola has been supporting the NAACP national and locally through the years."
At 44.1%, non-Hispanic blacks have the highest rates of obesity in the United States, according to the Centers for Disease Control and Prevention. Mexican Americans have the second-highest at 39.3%.
At a hearing in New York City Wednesday, an attorney representing the American Beverage Association laid the groundwork to request a stay of the ban, according to American Beverage Association spokesman Chris Gindelsperger.
"For an unelected board of political appointees to make decisions that will seriously harm the family-owned businesses I grew up with is unacceptable," said Councilwoman Letitia James, who has also filed an amicus brief in support of the American Beverage Association's suit, in a statement after Wednesday's hearing.
In opposing the ban, both the NAACP and the Hispanic Federation stress that they acknowledge that obesity is a major problem for their respective communities, but that the ban is the wrong approach to the issue.
"We've been screaming bloody murder for decades now" about an obesity crisis in the Latino community, Davila said.
In their court filing, both groups contend the problem would be better addressed "through education and community programs" that "encourage physical activity and a balanced diet."
In addition to justifying the proposal on health grounds, Bloomberg has cited cost-saving as an impetus for the policy. New York City spends an estimated $4 billion each year on medical care for overweight people, the mayor has said.
CNN's Mary Snow contributed to this report