According to William Chappell's 'Popular Music of the Olden Time' Vol 2 pp686-689, the tune was written by Dr Arne for the masque Alfred and given its first performance on the 1st August, 1740. Says Chappell, 'The words of the masque were by Thomson & Mallett, but Thomson seems to have taken the lead in the affair, since, in newspapers of the day, he alone is mentioned as the author'. As for 'Mar-i-ed to a Mer-mi-ed', well you'll find a version of it in the Burl Ives book of Sea Songs (Ballantine 1956 pp122-123, also in 'Chantying Aboard American Ships' Frederick Harlow. I dont know much about the second version - apart from singing it - but I got that version from an old recording of John Foreman's called 'The 'Ouses in Between'. Burl Ives also recorded it on an LP called 'Down to the Sea in Ships', I think. Somehow the name of Charles Dibdin seems to suggest itself to me as th author.