Recently I had occasion to walk someones line and I got stuck at William Parker. In one location I find him marrying Lucy Spaulding in Carlisle Mass in 1780. In another I find him marrying Hannah Dutton in Billerica Mass in 1773. That confusion has been propagated in the geneologies of FamilySearch where in about 20 submissions he marries either Hannah or Lucy. I can't find much on Hannah, but according to those submissions, she died in 1816 - that would throw out a first/second wife scenario.
William is either the son of Benjamin and Mary born in Billerica in 1757 (which makes sense), or the son of William and Sarah (Foster) born in Chelmsford in 1751. I believe the Chelmsford one is the one who married Hannah Dutton, while the Billerica one married Lucy Spaulding. There are 6 other contemporaneous William Parkers. The one born in Reading in 1760 would be the one who married Sarah Damon. The one born in Andover in 1755 would be the one who married Mary Hovey of Boxford. The other 4 I come up empty on (Reading 1759, Oxford 1754 (died 1756), Boston 1755 and Methuen 1754)