Burke's does not name William a son of Archibald, but does state that William Douglas is of Cavers and (on another page) that Archibald is the founder of the Douglas/Cavers line, so William is a direct descendant of Archibald. Given the dates, there is not much room for another generation between William and Archibald.
Sources: Title: Burke's Peerage & Baronetage, 106th Edition, Charles Mosley Editor-in-Chief, 1999 Note: DATE 2000