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Sweeny, Texas. Sweeny is a city in Brazoria County, Texas, United States, the westernmost incorporated town in the county. The population was 3,684 at the 2010 census. The city's motto is A City With Pride. The city is also known as Adamston.
Kenedy County is a county in Texas. It covers 1,946 square miles (1,245,184 acres), which represents less than one percent of the state total. Of the 254 counties in Texas, Kenedy County ranks 252nd in terms of the size of its population (407, according to 2015 Census estimates).