Son of William Maxwell (1703-1760), 2nd of Springkell, and Catherine Douglas (d. 1761), dau of William Douglas, 2nd of Kelhead. Married (1764) to Margaret 'Peggy' Stewart. They had at least 6 children. Sir William was Boswell's first cousin once removed, Catherine Douglas being Boswell's first cousin on his mother's side.
Boswell stayed with Sir William and family at Springkell from October 7 to October 13, 1762. On this occasion, he described Sir William as "a man of a handsome figure and genteel air, [who]carries in his external appearance the character which is much talked about and seldom found, a gentleman. He has a great deal of good sense, sweetness of disposition, and delicacy of taste. He is perfectly easy and polite, and may be styled, in every sense of the word, a pretty man".
Boswell also met with Maxwell at few times in London, shortly before he left for Holland in the summer of 1763. Margaret Stewart, who married Maxwell in the spring of 1764, was an early love interest of Boswell, who seriously considered marrying her during his first months in Holland. When Boswell received news of her marriage to his cousin it galled him, i.e. it made him bitter.1