Here's what I have collected ot date, any additional info appreciated.
Probably one of the Loyalist Applebys (son of?) who settled in the south of the province. He was living on the North West Branch (Miramichi) by 1801 and married Jane (Rogers) Hubbard at around that time. About 1814, he and the family resettled in Nelson parish, where they remained
APPLEBY, BENJAMIN -Sgt., N.J. Volunteers. From N.Y. to Saint John, N.B. -(Ref. 1) -lot 3, 100 A., S. side Washademoak Cr., Wickham Parish, Queens county, N.B. (originally granted to Garret Jacobus & others -see John DeLONG.) Would this be Benjamin's father?
Came to NB in 1782 per 1851 census.
Benjamin, who entered the Province of New Brunswick in 1782, was one of the Loyalist Applebys, five of whom (including Benjamin) settled on Lake Washademoak in 1785. He was on the North West, Miramichi, by July 17, 1801, when he purchased Lot 19 at South Esk, and it must have been about this time that he married Jane Rogers, the widow of George Hubbard, because they had five children by 1810, according to a petition which he filed that year. In the petition he gave his age as 35 and stated that he was the guardian of several of his wife's children as well as his own.
Benjamin received a grant of Lot 4 at Strathadam in 1808, but he lived on an adjacent property during most of his years in North Esk. While there he held the minor parish offices of Fence Viewer and Comissioner of Roads. In his petition in 1810, he requested grants for himself and his eldest step-son, Joseph Hubbard, on the South West and the family relocated there about 1814.
However, on March 17, 1803, at the meeting of the Court of General Sessions of the Peace, Benjamin was appointed a constable in the South West District which rather indicates that he was living there at the time.
The lot of land which Benjamin purchased on the South-West Miramichi was purchased from William Baldwin and his wife, Elizabeth, for 110 pounds of lawful money the 24th day of July, 1811, according to records at the Registry Office in Newcastle. The lot was bounded on the lower or easterly side by a lot granted to John Wilson. .........Benjamin apparently disposed of this property later as he died at the home of his daughter, Mary (Appleby) Vye (wife of John Vye), I believe, at Wilson's Point in the Parish of Derby in 1851. His wife, Jane, had died in 1823. Wilson's Point is now a historical site known as "The Enclosure". (The above was written by Florence (Appleby) Traer in 1995.)
Florence did provide some of her reference material.
Her source of information for his birth date was: 1) Petition filed after July 17, 1801, in which he stated that he was 35 years of age 2) Provincial NB Archives and NB Museum - states that he was a Loyalist from New York