 He left no children.In his funeral sermon he is stated to have suffered not only from the persecution which raged against the silenced ministers, being ‘several times brought into trouble and imprisoned,’ but from grievous bodily affliction; he had ‘been dying many years.’

Eaton and his Dukinfield colleague Timothy Taylor entered into sustained controversy with Richard Hollingworth, and Eaton later attacked the theology of both the antitrinitarian John Knowles and the Quakers.Eaton's writings were favourably regarded by the council of state, who, convinced of his ‘merit and good affection,’ augmented his stipend on two occasions (ib.