E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
is do up. Thus Ophelia says, in one of her snatches, he dupt the chamber door, i.e. did up or pushed up the latch, in order to open the door, that he might let in the maid (Hamlet, iv. 1). A portcullis and some other doors were lifted up or dupped.
Iche weene the porters are drunk. Will they not dup the gate to-day.Edwards: Damon and Pithias (1571).