In 1844 Sweeny married Diana Francis Haynie, a native of Knoxville, Tennessee. They had five children. In 1850 their Brazoria County property was valued at $4,140. In January 1851 Sweeny was involved in a legal dispute over the ownership of a number of slaves that was argued before the Supreme Court of Texas. By 1860 he was a wealthy planter with $32,000 worth of real estate and $43,000 in personal property, including thirty-nine slaves, in Brazoria County. The topsoil on his plantation is said to have been twenty feet deep. At the time he employed a full-time overseer and a tutor for his children. Sweeny died at La Grange, Fayette County, in 1869 and was buried near the southwest Brazoria County community of Sweeny. His widow died in Angleton in 1904.
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