From the Revolutionary War Widow's Pension Papers she signed in 1838, Lavintyea (Winche) Van Nosdall Beagle, wife of Revolutionary patriot, John Beagle, stated that her (maternal) grandparents, John and Fanny Vermilyea, were present at the wedding in 1785. (There was no mention of her parents being there.)
Using an online depository of old newspapers, I checked for articles about the surname Vermilyea. Two advertisements concerning sales of land were found in 18th century New York newspapers.
An ad, posted by Isaac Vermilyea on March 20 and 27, 1769 in the New York Gazette and Weekly Mercury, described a farm "situate near King's Bridge..." Among the articles included in the purchase was a "Quantity of Weavers Utensils."
Another ad, written by a Philip Vermilyea, Cortlandt Town, March 14, 1794 and posted in Greenleaf's New York Journal on March 26 and 29, 1794 described "A very Convenient place and good stand for a mechanic, whether Weaver, Black-Smith, Tanner, or Currier, being situated on the banks of the Hudson...about two acres of land...There is on the premises, a new framed house...and a log building, which has been improved as a weaver's shop."
It appears that at least a part of the Vermilyea clan was engaged in the craft of weaving. Did a member of that family teach John Beagle the weaver's craft? Is that the Dutchess County connection I have been searching for?