The National Alliance for Hispanic Health and nine other entities filed a brief Monday. They're calling the rule a "reasonable and measured attempt" at stemming a tide of obesity, diabetes and other illnesses.
The group says those problems are prevalent in minority communities where beverage companies target their marketing to particular ethnic groups.
New York's ban on purchasing soft drinks larger than 16 ounces is on hold pending an appeal. A hearing is scheduled for June 4.
The American Beverage Association represents soft drink companies.
A spokesman says it's received support from numerous groups and is confident the court will uphold a ruling that the city overstepped its authority.