Son of Alexander Maxwell (d. 1730), 2nd Bart of Monreith, and Jean Montgomerie (1689-1745), daughter of the 9th Earl of Eglinton. Married to Magdalene Blair of Blair (d. 1765). The couple had six children, among them Jane (1746-1811), later Duchess of Gordon, and Eglantine, Lady Wallace.
The Scottish city of Port William was founded by and named after Sir William.
Boswell mentions him in his journal of September 24, 1762, when Sir William visited the Herons at Kirroughtrie at the same time as Boswell. Boswell described Sir William as "formerly [...] a genteel, pretty-looking man. Now he looks like an overgrown drover. He entertained us with many of the exploits of his youth, which however were rather a little too marvellous."