Were you able to locate his will? My book, A CALENDAR OF DELAWARE WILLS, NEW CASTLE CNTY 1682-1800 had no will abstract for a John WITHERSPOON. ( Book was by Colonial Dames of Delaware, 1911, NY,reprint 2000, Genealogical Publishing Co)
The only WITHERSPOONS were:
Robert WITHERSPOON. Minister. St George Hundred. 04 Jun 1718. 22 Aug 1718. C:142 Rebecca PREMSON; wife Mary WITHERSPOON; Elias & Sedyer NAUDAIN, son & dtr of Sedyer NAUDAIN. Exec: Mary WITHERSPOON, Elias NAUDAIN, Isaac VIGOREAUX.
Flora WITHERSPOON. St George Hundred. 30 Oct 1772. 22 May 1781. L:244. Three grnddtrs: Hester MOORE, Mary MOORE, Susannah MOORE, dtrs of James MOORE; son John and Thomas. Exec: Isaac MOODY, Andrew BRYAN.
Sleighter BOUSHELLE, MD.Formerly of Cecil cnty, MD, but for some yrs of Burke cnty, NC. 14 May 1795. 16 May 1797. O:233 Nephews, sons of brthr, Thomas BOUCHELLE, John, Sleighter, Jr & Peter BOUSELLE; 5 grndchldrn: David, Thomas, John, Mary & Martha WITHERSPOON, chldrn of dtr Susanna WITHERSPOON; niece, Mary BOUSHELLE. Exec: James BYARD, John CARNAN, nephew Sleighter BOUSHELLE Jr.