William Roberts gave his age in 1812 as 46 years old. Since neither William or Catherine are found on the 1830 census, but are possibly alive in 1820 (as over 45), it is safe to assume that Catherine Rogers Roberts could be born no later than 1775. Given that William Roberts has 2 males over 16 (or 18) in 1802, then it would seem that if this is his eldest son, William's first child was born 1784-1786. Assuming a marriage at age 12-14 isn't common for women of this time frame. Even marriages at 15 or 16 weren't all that common, in fact, except among the Quakers, historians give the median age of marriage as 18-20 with husbands (at their first marriage) about 2 years older. Marriage when the wife was pregnant was common. If William was born 1766, and his eldest child was born 1784-1786 (based on the taxlists), then Catherine Rogers should be born 1765-1770.
I thought that at one time I had read that Catherine Rogers was the second wife of William Roberts, so that all of the children (or their heirs) named in the lawsuit brought by the children of Joseph Rogers wouldn't necessarily be children of Catherine Rogers, but of William Roberts. I can't find that now.
The heirs of William Roberts can best be determined from the lawsuit in which the children of Joseph Rogers name them in 1842.
Chancery Order Book 1 – 1832-1868 – page 90 – Lee County Virginia
At Rules held in the Clerk’s office of the Circuit Superior Court of Law and Chancery, for Lee County, on Monday the 7th day of November 1842.
Henry Rogers , Edley H. Rogers , William M. Davis and Louisa his wife, formerly Louisa Rogers and Thomas Russell and Lucinda his wife , formerly Lucinda Rogers heirs at Law of Joseph Rogers , deceased.
Complaint against: James Roberts , William Roberts , Thomas Roberts , John Robert s , Jesse Roberts , Emanuel Roberts , George B. Roberts and Jesse Robinett and Susan his wife, heirs of William Roberts, deceased and Emanual Roberts , Elizabeth Roberts and Joseph Roberts , heirs at law of Joseph Roberts, deceased and George Rogers , Commodore Rogers , Mary Rogers and Joseph Rogers , heirs of Elizabeth Rogers , deceased. And Sally Lawson , Peggy Lawson , Susan Lawson and Catherine Lawson , heirs of Mary Lawson , deceased. Defendants
The defendants, James Roberts , William Roberts , George B. Roberts , George Rogers , Commodore Rogers , Mary Rogers , and Joseph Rogers , not having entered their appearance and give security according to the Act of Assembly and the Rules of this Court and it appearing from satisfactory evidence that they are not inhabitants of this commonwealth, it is ordered that the Defendants do appear here on the first Monday in February next and answer the bill of the complaints and that a copy of this order be forwith inserted in some public newspaper published in this commonwealth for two months successively, and posted at the front door of the Courthouse of this County
Thus we have for William Roberts a son William Roberts who was the father of James, William, Thomas, John, Jesse, Emanuel, George B and Susan Roberts Robinett. He also has a son Joseph Roberts, father of Emaunel, Elizabeth and Joseph Roberts. He has daughters Elizabeth who married Adenstone Rogers and had George, Commodore, Mary and Joseph Rogers, and Mary who married a Lawson and had Catherine, Sally, Peggy and Susan.
William Roberts, Jr's son Jesse Roberts was born 1804 from the census of 1850 in Lee County, his son Emmanuel Roberts appears as a head of household in 1830 as age 20-29, so he also was born 1800-1810. Susan Robinette is found in Scott County, Va as born 1810. Thus, William Roberts Jr, should be the eldest son who was enumerated in 1802.
Joseph Robert's son Emanuel was born in 1823 according to Phillip Roberts a researcher, and Joseph Roberts was born in 1790. His widow, Margaret is listed as a head of household in 1830 Lee County with a daughter under 5, a son under 5 and son 5-10, which fits with the number of children named in the lawsuit.
Adenstone Rogers born in 1803 is the father of the children of Elizabeth Roberts. He must be a son of the older Adenstone on the taxlists (see Eleanor's comment) These children, Commodore, George, Mary and Joseph were born 1823-1831. In 1830 we find Adenstone Rogers in the Lee County census with a wife age 30-39. I have not been able to determine who exactly is the husband of Mary Lawson.
So we have for William Roberts we have the following
William Roberts Jr born about 1785
Joseph Roberts born about 1790
Elizabeth Roberts born 1790-1800
Susan Roberts 1790-1810.