I note their children were born in Hillmorton.
John 1737, Elizabeth 1739, Mary 1740, Sarah 1748, Thomas 1750.
Sadly the baptisms do not give any detail on occupations, which later records did.
If this is Mary Atkins below it suggests they did not follow the English naming pattern, this may make it more difficult to be clear on John. Movement between places in that period was not uncommon, especially if the were involved in agriculture, land owners would move people around. 
Mother   Ann Atkins
Father   Thomas Atkins
Birth   14 Jun 1713
Baptism   28 Jun 1713 Hillmorton, Warwickshire, England
A John Watts probate is listed on Ancestry but only that below?
Record Type   Probate
Death Date   Abt 1768
Death Place   Hillmorton, Warwickshire, England
Probate Year   1768
Jno Watts   Burial   30 Aug 1768   Hillmorton
Colin
Perhaps you could post the criteria linking John to Yardley Hastings.