From:  Find A Grave

Birth: Dec. 12, 1617, EnglandDeath: Apr. 17, 1694
Essex
Essex County
Massachusetts, USA
The maiden name of William BALLARD's wife, Grace, has long been controversial, for there is no direct, primary record proving what it was. However, there is enough circumstantial evidence make a case that she may have been Grace BERWICK, daughter of Thomas BERWICK and Anne BLOUNT. 

To begin with, all the parties were in the right place at the right time (Andover in the 1640s) and were the right ages with the right names. In other words, we don't have to torture the data to make anything fit and nothing in the data disproves the connection. There is no question that these families were in contact because William & Grace's daughter, Elizabeth, married Anne BLOUNT's nephew, William BLUNT, and William & Grace's great-grandson, Thomas ABBOTT, married Lydia BLUNT. And we have to ask these questions: 

If Grace BERWICK didn't marry William BALLARD, whom did she marry? There is no record of her marrying anyone else. 
What other "Grace" was there in Newberry or Andover for William to have married? 
These were very small towns. If my memory serves me — I can't find the source at the moment — the population of the entire Massachusetts Colony at this time was only about 600 families, and William was one of the earliest settlers of Newbury (he is 16th on the list of first settlers), when the town was at its smallest. So, just how many unmarried "Grace's" — about the same age as William — could there have been in this tiny settlement? And we know the families knew each other. Thank heavens she wasn't named Sarah or Elizabeth or this would be hopeless!