Hi Osborn
You would have increased your chances of success by posting this on the Beds board as all of the parishes you mention are/were in Beds including Eaton Socon. People with Beds parish register transcripts do not necessarily read the Cambs board.
Most of Beds pre 1812 has been extracted onto the IGI (
www.familysearch.org) so a lot of Beds research can be done yourself online, although the IGI should only be treated for what it is - an index. There's no substitute for checking the parish registers which can be viewed at your nearest LDS Family History Centre.
Working backwards:
there are burials in Thurleigh as follows:
John Osborn age 84 on 31 March 1837
Elizabeth Osborn age 62 on 10 Sept 1813
So the death of Elizabeth fits with the marriage of John Osborn to Mary Green in 1815 although you would need to check with the parish register to see if he was a widower.
There was only one child christened to John and Elizabeth in Thurleigh, Samuel on 30 June 1793 (and he was buried on 11 Aug 1793 but again you'd need to confirm with the parish register as no age is given), so it looks as though they arrived in Thurleigh around 1792/3 as this is the first Osborn occurrence in the parish. Presumably there were other children born between c1775 and 1792, and there are three christenings in Eaton Socon of John Watts Osborne in 1785; William in 1788 and Jane in 1789 which might be them.
A John Osborne, son of William and Abigal was christened in Eaton Socon on 5 Oct 1755.
But I can't see a marriage of John and Elizabeth in Beds that fits. I wonder if John Watts Osborne is a clue to Elizabeth's maiden name? (although in 1851 he was John Potts Osborn living in Thurleigh which may be an enumeration error). Again you'd need to check the Eaton Socon register to see if it was Watts or Potts.
Interesting - there's an Elizabeth Watts christened on 1 March 1752 at Thurleigh, which might be a complete coincidence, but....! It could help explain why they moved to Thurleigh from Eaton Socon. But I still can't find a marriage for Elizabeth Watts.
Eaton Socon was on the border with Huntingdonshire, so I've checked the Hunts Marriage Index with no success.
So I've drawn a blank with the marriage of John and Elizabeth, although I have a hunch as to who she might have been, but it's no more than a hunch.
Turning to John's father William
Have you checked Colmworth parish register to see if there's any extra detail on the 1739 marriage? It probably just states William Osborn and Abigail Garner, but you might be lucky and find it has "William Osborn of Eaton Socon", or wherever).
There is no obvious christening on the IGI (pre 1837 you are only likely to get baptism details, not birth) so he could have been born outside Beds, or the family was non-conformist and he wsn't baptised in the established church.
They seem to have had all their children in Eaton Socon, Beds, which is only 3 miles from Colmworth, so possibly William's parish of residence was Eaton Socon, although there's no baptism for him there - in fact there are no baptisms of Osborns in Eaton Socon before William and Abigail's children, but there are burials of John Osborn in 1729 and Carola in 1732. A long shot but I wonder if these might be William's parents? It might be worth your while to check out this possibility as you have nothing to lose - it's the only clue I can see.
Hope this gives you some ideas
Regards
David