Fanny's father was Rev. David Roper (b 27 Sep 1792 - Charles City County, VA; d 28 Feb 1827 - Charles CIty County, VA) and her grandfather was David Roper (b 13 Nov 1744; d 16 Apr 1808 - Charles City County, VA). The lineage gets murky before that although we are reasonably confident that the great grandfather was John ROPER (b 1709).
The published biography of Fanny's father Rev. David ROPER (from 1838) is posted at this thread:
"Biography of Rev. David Roper, of Richmond, VA" (14 Mar 2002 3:48PM GMT)http://boards.rootsweb.com/surnames.roper/461/mb.ashx
The ROPER and YATES families have been closely allied for more than four centuries. The specific identity of Fanny's grandmother is UNKNOWN, though some researchers have made speculative ascriptions WITHOUT ANY SUPPORTING EVIDENCE.
The ROPER family plantation on the Chickahominy River in Charles City County, surveyed in 1705 and Patented in 1714 was in respect of the transportation of several persons into the Colony, including an Elizabeth YATES. Captain William ROPER transported William YATES into Virginia in 1633 or 1634.
The ROPER family is intermarried with the YATES family in OTHER branches of the family in generations AFTER David ROPER (b 1744, d 1808), but these are OTHER BRANCHES of the ROPER family. Since the identity of Fanny's grandmother and great-grandmother are UNKNOWN, I cannot state with certainty that there is NOT a YATES connection. But there is NOT a KNOWN connection. I hope this helps!
Perhaps you can share with us your interest in Fanny and a possibly YATES connection.