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.

Read - Groups: NYC soda ban unfair to small, minority-owned businesses

Previously - How I kicked my Coke habit