"Thwaite", is the Norse word for a field so this doesn't take much working out.
Part of the area is called "Hallthwaites". Hall (Norse - hallr) is a relative of the Indo-European word for high. Hence "high fields". The word hall (as in a building) is related in that in the Middle Ages, the lord of the manor almost invariably lived at the top of a hill in a "hallr".