If anybody is still looking at this page, here is my research:
William Checkley (the spelling changed to Cheakley when he moved north) was born in Kite's Hardwick, Warwickshire and christened in the local parish church at Leamington Hastings on 6th October 1782 (might have been a late baptism). He was buried in Skipton on 8th June 1837. His father, also William, was married in Leamington Hastings on 21st June 1779, to Elizabeth Meeke. William senior moved to Ashford in Kent, date unknown. In the 1841 Census he is living with his daughter Ann, both born out of county. By the 1851 and 1861 Census, William has died (1844) but Ann and her sister Mary gave their birthplace as Hardwick, Warwicks, which enables the family to be found. William senior's age at death gives a birthdate of circa 1760. There are no William Checkleys born in Leamington Hastings/Kites Hardwick at this time but there is a likely birth at Ryton on Dunsmore (bpt 5th April 1761, s. of Thomas and Ann).
There are 12 surviving settlement certificates for Leamington Hastings (Warwicks Archives ref. DR0043A/96-106) which I checked in December and none relate to the names Checkley or variants, so the link with Ryton on Dunsmore cannot be proved.