Facts and Events
James and his wife Mary were found on the records of Rahway/Plainfield Monthly Meeting along with James' brother William and William's wife Prudence. All their names were spelled 'Jacson'. These two families were the only Jacsons recorded in the Rahway/Plainfield Monthly Meeting record of births. <http://members.tripod.com/PlainfieldFriends/birthreg.htm>
I found the above 'Jacson's at the Quaker Plainfield/Rahway/Woodbridge Monthly Meeting; and James is married to a Mary; and later found R. G. Clarke's work which he takes from the NYG&BS Record, Jan 1962, pg 36 & 166; a well recognized source. Mr. Clarke records that James was first married to Sarah Thorne and after she died he remarried two times; first to Mary Thorne and later to Mary Fitz Randolph. Nothing so far is known about the parents of Mary Thorne, nor the dates of her birth or death. But we know that James' first wife Sarah died in 1737 and he married Mary Fitz Randolph in 1749; therefore, the children found with 'James Jacson and Mary' must have been children of Mary Thorne.
Mary Fitz Randolph was widow of William Thorne, son of Joseph Thorne. Mr. Clarke also records that James and Mary were Quakers. And since James and William were found in this Monthly Meeting together, it makes good sense to me that these were brothers, sons of James Jackson and Rebecca Hallett.
From Essex County New Jersey Quaker Records @ ancestry.com:
The child Sarah, born 11 Jan 1740, has been attributed on many charts to be the daughter of William Jackson. It looks to me that this is not correct. It appears that she is the daughter of James and his second wife, not his brother William.