The identification of Elizabeth Weaver (63) seems fairly certain.
The Census for 1851 shows that she was born in Hanbury in about 1813.
There is a baptism for Betsy Weaver at Hanbury on 3 Jan 1813.
This seems a fairly good fit and if this is correct her parents were George Weaver and Mary.
There are six other baptisms for children of George and Mary in Hanbury.  They are not the only family named Weaver in Hanbury at this time however.
Therefore the identification of George seems fairly certain.
However, his birth and parents have not been identified.
 

Family search yields only one George Weaver baptised in Worcestershire between 1760 (George would be about 34 when married) and 1780 (George would be about 14).
This took place in Eastham, which is about 20 miles west of Hanbury on 3 April 1777.
The parents of the child were William and Elinor Weaver.  This couple had six other children baptised at Eastham.
  

A search on FamilySearch reveals only one marriage for George Weaver and Mary in Worcestershire between 1790 and 1810.
This took place on 13 November 1794 in Stoke Prior which is adjacent to and north of Hanbury parish, the bride being Mary Tayler. George was of the parish of Stoke Prior whilst Mary was of the parish of Hanbury.
There are no others baptisms to children of George and Mary Weaver around this time in Worcestershire.
Their first child was baptised in July 1795 (less than 9 months after the wedding) and thereafter at regular intervals until Betsy (Elizabeth).
  

There appear to be no George Weavers in the 1841 Census born between 1760 and 1780.
There are three Mary Weavers in the 1841 Census for Worcester, two listed as age 70 in Drotiwich Union and one listed as 65 in Worcester.
These three also appear in the 1851 Census:
One was in Worcester district, aged 80 (born c1771)  (would be 23 in 1794)
One was in Pershore district, aged 77 (born c1774)   (would be 20 in 1794)
One was in Droitwich district, aged 75 (born 1776)  (would be 18  in 1794)

The first Mary was with her husband John.
The second Mary was living with her son William and was said to be born in Bewdley in 1774. Another child, Marey was also living with them.  William was born in Kidderminster and Marey in Stowe.
The third Mary was living in Old House, Hanbury and was a "Farmer of 200 Acres Employing 5 labourers".  She lived with her son Daniel who was unmarried and born in about 1805 in Hanbury. Mary was born in Claines.
There is a baptism for Daniel Weaver in Hanbury but in 1799 (born 14 Apr 1799). His parents were William and Mary Meaver, and therefore appear to be a different family.

Therefore, notne of these three seem to be the correct Mary Weaver.