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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.
Sweeny is 30 feet (9.1 m) above sea level and is 20 miles (32 km) from the Gulf of Mexico. The San Bernard River flows 1-mile (1.6 km) east of city limits. The town is in a dense forest on coastal plains. Sweeny is at the intersections of Farm Roads 1459 and 524. The town is accessible from Highway 35 by taking 1459 or 524, which intersect in Sweeny 5 miles (8 km) from the highway, forming a loop from 35. Brazoria County Road 332, known as Ashley-Wilson Road, is also a main thoroughfare through the city.