Newman married Anne Mary Burwell (nee Anne Mary Brooke, AKA Mary Marshall Brooke) 22 Feb 1826 in Fauquier Co, VA.
Anne Mary first husband was William Nelson (Nathaniel) Burwell (4/23/1791 - 8/2/1822). They were married 4/1/1811, also in Fauquier Co.
See also "Gleanings of Virginia History: An Historical and Genealogical Collection" page 270.
Web address is http://books.google.com/books?id=CP8RAAAAYAAJ&vq=Alexand...
She died 5/15/1836. No info on place of death/burial, although Alexander Newman buried at Mount Rose Cemetery, Moundsville, Marshall Co, WV and Burwell buried at Old Chapel Cemetery, Millwood, Clarke Co, VA (which I believe is now WV).