Who and what are you looking for in Witton Gilbert?
Matthew Newby and Frances Lawson married at Little St. Mary's Durham 25 Feb 1748, both of this parish, entered in the Witton Gilbert parish record. There are many such entries for marriage at Little St. Mary's Durham
The baptisms you find in the IGI extracted records are as they are in the parish record. Father's name and mother's first name, no place of birth or occupation of the father. So those records are as complete as they are going to get.
Ther are no Newby's or Whitehaead entries from 1813-1839 in Witton Gilbert.
Burials:
27 Oct 1753 John son of Matthew and Frances Newby
25 july 1764 Frances daughter of Matthew and Frances Newby
20 Jan 1772 Matthew Newby
Frances Newby, died 24 Dec 1807, buried 27 Dec 1807, age 86, widow of Matthew Newby, woodman, and daughter of John Lawson, tailor.
this could be Frances' mother: burial Elizabeth Lawson, wife of John Lawson 16 Jan 1763
John Lawson, the elder, 21 Nov 1763
Hope this helps,
Janis