NEW YORK -- At barbecue joints, coffee counters and bottle-service nightclubs, a coming clampdown on big, sugary soft drinks is beginning to take shape on tables and menus in a city that thrives on eating and going out.Some restaurants are ordering smaller glasses. Dunkin' Donuts shops are telling customers they'll have to sweeten and flavor their own coffee. Coca-Cola has printed posters explaining the new rules, and a bowling lounge is squeezing carrot and beet juice as a potential substitute for pitchers of soda at family parties -- all in preparation for the nation's first limit on the size of sugar-laden beverages, set to take effect Tuesday.Some businesses are holding off, hoping a court challenge nixes or at least delays the restriction. But many are getting ready for tasks including reprinting menus and changing movie theaters' supersized soda-and-popcorn deals.At Brother Jimmy's BBQ, customers still will be able to order margaritas by the pitcher, cocktails in jumbo Mason jars and heaping plates of ribs. But they'll no longer get 24-ounce tumblers of soda, since the new rule bars selling nondiet cola in cups, bottles or pitchers bigger than 16 ounces."Everything we do is big, so serving it in a quaint little 16-ounce soda cups is going to look kind of odd," owner Josh Lebowitz said. Nonetheless, he's ordered 1,000 of them for the North Carolina-themed restaurant's five Manhattan locations, rather than take on a fight that carries the threat of $200 fines."As long as they keep allowing us to serve beer in glasses larger than 16 ounces, we'll be OK," Lebowitz reasoned.Beer drinkers can breathe easy: The restriction doesn't apply to alcoholic beverages, among other exemptions for various reasons. But it does cover such beverages as energy drinks and sweetened fruit smoothies.City officials say it's a pioneering step to staunch an obesity rate that has risen from 18 to 24 percent in a decade among adult New Yorkers. Health officials say sugar-filled drinks bear much of the blame because they carry hundreds of calories -- a 32-ounce soda has more than a typical fast-food cheeseburger.The city "has the ability to do this and the obligation to try to help," the plan's chief cheerleader, Mayor Michael Bloomberg, said last month.Critics say the regulation won't make a meaningful difference in diets but will unfairly hurt some businesses.