I am descended from Clisby Cobb (1748-1815). He was born in Morris County, New Jersey, the son of John and Rhoda Cobb. His migration pattern parallels that of your family. Clisby Cobb went to Surry County, North Carolina, in the 1780s, then moved on to Lincoln County, North Carolina, where he died.
Given the name, I feel sure that his mother was a granddaughter of James Clisby the Scottish immigrant and his wife Elizabeth Burwell. Some researchers say that Rhoda Cobb was a Smith, in which case her mother would have been a Clisby. Other possibilities are that Rhoda was the daughter of an unknown (to me) son of James Clisby, or that she was a daughter of Amos and Mary (Clisby) Whittemore. Can you help?