He was born in 1764 at Wrexham, to John Waithman, a joiner at the Bersham Ironworks, and Mary (née Roberts).
Waithman’s father was a native of Warton, Lancashire, evidently of Quaker antecedents, who came to the Bersham furnace in the wake of Isaac and John Wilkinson the iron-masters, when (by 1756) they moved from Backbarrow near Furness to Bersham.
He married Mary Roberts at Wrexham 29 January 1761, but Waithman’s baptism is not recorded there.
His father died soon after his birth and in 1776 his mother remarried at Wrexham, Thomas Mires, furnaceman, and had a second family, whom Waithman subsequently supported.
The boy was placed in the care of an uncle.