In 1746 she married to Agmondesham Vesey of Lucan, a wealthy cousin and a Member of the Irish Parliament for Harristown, County Kildare, and Kinsale, County Cork, He was accountant-general of Ireland.
They had no children.
Agmondesham was continuously unfaithful to Elizabeth but she maintained the façade of a happy marriage. She nursed her husband through attacks of epilepsy, but depended for her support upon a circle of female friends.
Her marriage meant Elizabeth split her time between London, England and Lucan in Ireland, but eventually settled mostly in London at houses in Clarges Street and Bolton Row, Mayfair.
In 1782 both her own and her husband's health began to fail; she feared she was losing both her sight and hearing and Agmondesham Vesey died on 3 June 1785.
Vesey and her closest friend Miss Handcock, sister of Vesey's first husband, were left facing relative poverty when they found that Agmondesham had left them nothing in his will, despite leaving £1000 to his mistress. At the time of their marriage Elizabeth had turned over all her own funds to her new husband. Their only income was Vesey's jointure and Handcock's annuity which together brought in about £800 a year.