"One of a new kind of puritans lately arisen, so called from their profession to live by rules and in constant method" [Johnson]. Protestant religious sect founded 1729 at Oxford University by John and Charles Wesley, took that name almost from inception, but it had been used since at least 1686 for various new methods of worship. Related: Methodism.[Methodist etymology, Methodist origin, 英语词源]
"pertaining to Wesley," 1771, in reference to John Wesley (1703-1791), founder of Methodism. The surname is from various places in England named West Leigh (or some variant). Related: Wesleyanism.