Witnesses to the marriage were John COGINS Maria BURGINS.

This is a major conjecture that this William Knibbs was the son of Hannah Knibbs. William suddenly appears in the 1851 census where it clearly states that he was born in Somerton, Oxfordshire, in about 1803. The 1861 census confirms the same place and date of birth, so I have no doubt that he was connected to this part of the family, but just how remains a mystery.
We know from the parish records of Somerton that the only Knibbs seen to be having children at that time in that parish Nathaniel Knibbs and his wife Elizabeth Kerrick who had 8 children in total, all of whom were baptised within the parish.
On the basis that there's no sign of a baptism for William, I believe it unlikely that William was a son of Nathaniel. However, Nathaniel had several older sisters, and we know for sure that Hannah didn't ever marry. So the suspicion is that William may well have been an illegitimate son of hers.
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In 1851, we see William living at Rocks Hill, Kingswinford, Brierly Hill, Staffordshire:
John Hickson Head Man 28 Boatman Oxford
Jane Hickson Wife Mar 24 Oxford
John Hickson Son 3 Kingswinford Staffordshire
George Hickson Son 6 months Kingswinford Staffordshire
William Knibs Lodger Mar Boatman Somerton Oxfordshire
Mary Knibs Wife 40 Somerton Oxfordshire
Emma Knibs Sister in Law 16 Kingswinford Staffordshire
Hanna Knibs Sister in Law 6 Kingswinford Staffordshire
Joseph Knibs son in Law 4 Kingswinford Staffordshire

Note that Jane Hickson is William's daughter. Emma, Hanna and Joseph are William's other children.
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In 1861, we see William living at Dock Street, Kingswinford, Staffordshire:
Samuel Price Head Wid 46 Cordwainer Hertfordshire Hertford
William Kibbs Lodger Mar 58 Boatman Oxfordshire Somerton
Mary Kibbs Wife 50 Oxfordshire Tackley
Joseph Kibbs Son 14 Boatman Straffordshire Kingswinford
Hannah Kibbs Daur 16 Staffordshire Kingswinford