Found by googling "I get in a weaving way." Chapman Family Papers, 1848-1881, mention "I get in a weaving way" as a song sent to William Chapman in the army (Civil War) by James Chapman, and "said to be a Negro tune." Another sent at the same time was "Things I Don't Like to See."

So far no luck. Not in Traditional Ballad Index, American Memory, Levy or Bodleian under that title.