HMS Weymouth was a 44-gun fifth rate of the Royal Navy. She was previously the East Indiaman Wellesley, built in Calcutta in 1797. She was purchased in May 1804, and fitted out between May and August that year at the yards of Perry & Co, at Rotherhithe. Further fitting was carried out at Woolwich Dockyard in November. She was then laid up in ordinary at Deptford in November 1821. Between February and October 1828 she was fitted at as a convict ship and sailed to Bermuda. Weymouth was finally sold there for £300 on 2 July 1865 and was broken up.