To fit with a counterweight.
A heavy mass of often iron or concrete, mechanically linked in opposition to a load which is to be raised and lowered, with the intent of reducing the amount of work which must be done to effect the raising and lowering. Counterweights are used, for example, in cable-hauled elevators and some kinds of movable bridges (e.g. a bascule bridge).
To weigh in at; to weigh.