John Bab(b)in(g)ton was born around 1608 died 1670 (PCC Wills 1661-1700) nil (LCC Wills 1660-1700)  shows that John was a husbandman of Benniworth, Lincolnshire, ref:W1670/ii/416 I172/193,  his will was dated 28 November 1670 and was proved at Lincoln 19 December on 1670.

Thanks to Wendy Atkin of Sleaford, Lincs for this information.   

Was his father Ferdinando or Cornelius (see Lincs page 2)?
This is a precise of his will.  
John BAB(B)IN(G)TON leaves to his son John BABBINTON and his children, three ewes (sheep) and three hogges (pigs).
To his daughter Esther [C]ASH he leaves 1 ewe and 1 hogge.  
To Mary HUTCHISSON (whoever she was in his life?) 4 ewes
To his son(s) Richard BABBINTON and William BABBINTON all the rest of my goods (made exors).  
John BABBINTON (his mark)  Witnesses Peter WILSON (his mark) and Waters WILSON (his mark).  

He married Anne? Who is not mentioned in his will (therefore likely died before 1670) 
Children of John BAB(B)IN(G)TON and Anne. 

1.  John BABBIN(G)TON christened on 20th April 1628 (died before 1632) at Torksey Saint Peter, Lincolnshire. 
2.  John BAB(B)IN(G)TON christened on 15th December 1632 at Butterwick (Holland) (South Lincs) died 1648 (shown in Bishop Transcripts, but difficult to decipher so could be wrong) in Benniworth, Lincs. 
3.  Elizabeth BABBIN(G)TON christened 1653 at Benniworth, not shown in will.
4.  John BABBIN(G)TON mentioned in John’s will, living in 1683. (christened 1664/54 in Benniworth)!
5.  Esther BABBIN(G)TON married …..[C]ASH mentioned in John’s will.
6.  Richard BABBIN(G)TON mentioned in John’s will.
7.  William BABBIN(G)TON mentioned in John’s will.
8.  Christopher BABIN(G)TON son of John baptised in Benniworth April 13th 1645/55 (Bishop’s Transcripts, not shown in will), my 8 times grandfather.

Interesting stuff!