I quote will quote at length from the 1977 Weemsana newsletter:
"Margaret, Countess of Wemyss and James, Lord Burntisland had at least six children and possibly more. Three sons and three daughters are known.
"David the eldest, baptized Apr. 29, 1678, became the 3rd Earl of Wemyss (4th if Margaret is counted)… [etc.]
"John the second son was baptized October 14, 1680, but no further information is available on John.
"William is believed to be the third son though no baptismal evidence has come to light. However, a letter written in April 1700 from the 1st Earl of Cromarti, who married Countess Wemyss after the death of Lord Burntisland, to George, 1st Earl of Melville states: 'I hope that I may have the honor to see you heer ether on Wednesday or Thursday. My Lady (Countess) Wemyss expects her three sonnes heer that day, I mean Thursday.' This letter has been accepted as definite evidence that Margaret, Countess of Wemyss, had three sons, as a letter from Lord Lyon, Register House, Edinburg, dated Aug. 3, 1962 attests: 'You do produce evidence now in the Cromarty letters that Lady Wemyss had three sons of whom only two are so far named.'
"William the third an youngest son of Margaret, Countess of Wemyss and Lord Burntisland, probably because of the British law of primogeniture, received no title or lands but became a colonel in the service of James Stuart, son of James II of Great Britain…. Colonel William Wemyss, father of our emigrant ancestor, was killed in the Battle of Preston on Nov. 12, 1715."
Was there a Col. William Wemyss fighting at Preston with the Jacobites? I'm not sure I have the resources to find out.
Register House, Edinburg, is listed as a source, among many sources for the article which traces the Wemyss family back to its origins.