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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.
According to our research of Texas and other state lists there were 21 registered sex offenders living in Sweeny, Texas as of February 12, 2017. The ratio of number of residents in Sweeny to the number of sex offenders is 178 to 1. Nearest city with pop. 50,000+: Brazosport, TX (20.0 miles , pop. 59,653).