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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.
Welcome. The City of Sweeny is proud to present this Web site for our residents and the surrounding community. Our motto is A City With Pride.. We are proud of our history, our government, and our community. We are continuously working to improve this Web site. Please send us your feedback by way of comments, suggestions, or other ways in which we can better serve you at info@ci.sweeny.tx.us.