Given the time 1767 and the location the British Province of New Jersey. The best approach would be to look at contemporary British usage. Given those starting points, Hon, typically indicates a non-titled member of a family with a seat in the house of Lords. For example if my Father is the Duke of Denver, and I am the 2nd son. I am entitled to use Hon before my name to indicate the heritage. On the death of my father, my older brother inherits the title Duke of Denver, and I remain an Hon. If my brother dies without issue, I then inherit the title and become the next in the series of dukes of Denver.
Current 21st Cent American Practice Hon. is part of the formal address of judges, Senators, and Representatives among many other public figures.
Apologies to Dorothy Sayers for borrowing her detective. I needed a made up peer to avoid creating problems and Lord Peter fills the bill nicely.