Some more names for you that might be part of the picture.
Baptisms from Uppingham Parish Registers
Christopher son of William and Mary Leaton 28 September 1803
Ann, daughter of Mary Leaton 13 July 1821 (No. 330) No father recorded.
Susanna Sysmey, daughter of Christopher and Mary Leaton, 4 January 1832 (No.761)
Elizabeth, daughter of Christopher and Mary Leaton 30 October 1835, (No. 536)
Burial records from Uppingham Parish Registers
Christopher Leaton aged 79, 15 February 1821 (No.243)
Elizabeth Leaton aged 67, 18 May 1819 (No. 202)
Christopher Leaton aged 34, 9 August 1838 (No.796)
Richard Leaton aged 2, 14 August 1827 (No.467)
William Leaton aged 70, 18 December 1841 (No.903) Abode Horninghold, Leics.
Marriage from Uppingham Parish Registers
This might be of interest given the name of one of Christopher and Mary’s children.
Charles Peach of the parish of Deenethorpe (modified by Crowboy 26/1) in Northamptonshire and Elizabeth Leaton of the parish of Uppingham by licence 4 October 1795
Witnesses Elizabeth Sismey and Christopher Leaton
Crowboy