Individual Details

Charlotte Helen says his wife is Alice Atwood; the Ballard book says James son of Benjamin married Alice Atwood. The probate of James married to Alice includes notes from Josiah and William -- and he is deceased before father -- but both the James's die before Josiah Ballard -- so do not know yet
The marriage of Alice Atwood is not until 1762 -- so maybe this one is Mary Robins since the other James is born about 1737
But the 1737 James was born in Lancaster and the marriage to Mary Robins was in Lancaster so that makes more sense -- so maybe they are just a young couple marrying in 1756. James Ballard and Mary Robins are both of Lancaster and Mary Robbins was born in 1738
So, I am thinking since the inventory of James of Alice includes notes from William and Josiah, I might go with Alice for the wife. The marriage of James and Alice is in Andover.

There are no children identified for James and Alice -- although Alice Ballard who married in Salem in 1789 is likely his child

The Essex Antiquarian agrees that this James married Alice
https://books.google.com/books?id=9Qg0Jnt4y-YC&pg=PA36&lpg=PA36&dq=alice+ballard+alexander+anderson&source=bl&ots=aLp4XoDAWK&sig=ACfU3U2EDUWP8k8ce5DmyWBlEevjL3tTwA&hl=en&sa=X&ved=2ahUKEwiQ7LH_9LrjAhVBJ80KHTyMDW8Q6AEwBnoECAkQAQ#v=onepage&q=alice%20ballard%20alexander%20anderson&f=false

Birth	3 Jul 1730	Andover, Essex, Massachusetts
Marriage	2 Jun 1762	Boston, Suffolk, Massachusetts - Alice Atwood
Death	1774	Salem, Essex, Massachusetts
Probate	1774	Salem, Essex, Massachusetts
Biography

Spouse	Alice Atwood (1739 - )
Child	Alice Ballard (1764 - )

Father	Josiah Ballard (1699 - 1780)
Mother	Mary Chandler (1701 - 1779)
Sibling	Josiah Ballard (1721 - 1799)
Sibling	William Ballard (1723 - 1782)
Sibling	Mary Ballard (1725 - 1750)
Sibling	Lydia Ballard (1727 - 1779)
Sibling	Hannah Ballard (1732 - 1824)
Sibling	Sarah Ballard (1735 - 1790)
Sibling	Phebe Ballard (1738 - 1815)
Sibling	Dorothy Ballard (1741 - 1813)
Sibling	Rebecca Ballard (1745 - 1777)

Notes