The paper gives a survey of the history of damping methods for balances. Representation on Egyptian drawings demonstrate that the person performing the weighing shortened the measuring time by holding the suspension cords and touching the beam. By means of delimiters, the Romans constricted the deflection amplitudes. In the 19th century, the movements of precision balances were damped with a brush. For analytical balances, locking mechanism were developed, often combined with levers lifting the weighing scales and the beam in order to relieve the knife-edges. Half-arresting was used to curtail weighings. Air damping was invented by Arzberger in 1875, and eddy current damping by Marek in 1906. In electronic balances, lag, lead and filter elements and absorptive attenuators are used. For digital balances, the fast-reacting nullification of eddy signals is applied. This revised version was published online in July 2006 with corrections to the Cover Date.