From multiple records it is clear that James Watson the Jacobite (d. ca. 1776) married Barbary , and that she was the mother of their known children. However her maiden name remains unknown. While it is often repeated without sources as "Parker", I assume that comes from the record of a (different and much later) James Watson marrying a Barbary Parker in Haywood County, NC on May 28, 1832 (source Haywood County Marriage Bonds).
Obviously this is far too late for the marriage date of James Watson the Jacobite and Barbary of Louisa. In fact, it is curious that James Watson is often stated, again with no sources, to have married Barbary in 1732. This is exactly 100 years before the Haywood marriage. I think it very possible that the original "researcher" saw the name James Watson, saw the unusual name of Barbary, and just changed 1832 to 1732 (while erroneously adding the Parker).