Weakley County is a county located in the northwest of the U.S. state of Tennessee. As of the 2020 census, the population was 32,902. Its county seat is Dresden. Its largest city is Martin, the home of the University of Tennessee at Martin. The county was established by the Tennessee General Assembly on October 21, 1823, and is named for U.S. Cong…Weakley County is a county located in the northwest of the U.S. state of Tennessee. As of the 2020 census, the population was 32,902. Its county seat is Dresden. Its largest city is Martin, the home of the University of Tennessee at Martin. The county was established by the Tennessee General Assembly on October 21, 1823, and is named for U.S. Congressman Robert Weakley. Weakley County comprises the Martin, TN Micropolitan Statistical Area.