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Born at Nine Partners, New York in 1776, he later moved to Danbury, Connecticut. He was a member of the Connecticut House of Representatives in 1818, 1820, and 1824 and also served in the Connecticut Senate 1826-1828.
Tweedy held many local offices before being elected as an Anti-Jacksonian to the Twenty-third Congress (March 4, 1833 – March 3, 1835). He died in Danbury, Connecticut, aged 92. He was buried in Wooster Cemetery.