The first thing to do is identify where Black Hadley or Hadleigh is in County Durham. Although I live in the county I don't recognise the name, nor can I find a reference to it. However, there is a place called Black Hedley just over the county boundary in the parish of Shotley, Northumberland. This appears in enough probate records to be sure it existed, but I haven't located it on a map.
There is a PhD thesis on Quakers in 17th century Durham and Northumberland, which you might find helpful for background. Its listing of Quakers includes mention of Thomas Layburne of Derwentcote, County Durham, in the 1666 Hearth Tax. Derwentcote is only a few miles from Shotley.
I'd therefore go looking in the area either side of the River Derwent (which is the county boundary).
There are a number of probate records for Leyb* or Layb* in that area (Muggleswick, Medomsley, Lanchester) in the North East Inheritance database. These are freely available online and would be worth investigating.
