I am interested in the Cape Fear River area of NC as my husband's ancestor Hanson Kelly Ruark, Sr. is from Southport, NC (formerly Smithville,NC) and we are unable to find parents or siblings.
I did a quick search using Henry Braswell name and on the BRASWELL-L archives:
"a water borne plague of some sort "wiped out The Cape Fear families by the dozen in 1761."
I was unable to find out any more information on NC History about this plaque - but many died of cholera, yellow fever, dengue fever, and other fevers ....some brought in by ships at Wilmington, NC, and others carried by people as they moved around.
It is possible that your Allens moved to Georgia to get out of the area due to disease.Or because land was being bought up and there was not enough land for families to pass on to their children.
Also the Revolutionary War caused some to move if they were Loyalists and "lost" in the War = which England lost.