His parents were John Starkweather and Lydia (Button) Starkweather of Preston, Connecticut. His father served in the War of 1812 as a private in Captain Isaac Nelsons Company. Henry was a first cousin to Brig. General John Converse Starkweather.
Henry served in the Connecticut Legislature in 1856 and was a delegate from Connecticut to the 1860 Republican National Convention, which nominated Abraham Lincoln, and to the 1868 Republican National Convention, which named Ulysses S. Grant. He was chairman of the Republican State Committee of Connecticut and a member of the National Republican executive committee. He was appointed postmaster of Norwich, Connecticut, in 1861 by Abraham Lincoln, and was reappointed by President Andrew Johnson again in 1865. He resigned in 1866 and was elected to US Congress in 1867 and served until he died in office in 1876.
- Starkweather, Carlton Lee (1904). Robert Starkweather and his Descendants, Knapp, Peck and Thomson.
- Henry Howard Starkweather. findagrave.com