Can you balance the weights?

An object is placed in the left pan of a double pan balance. You do not know its weight, except that it weights a whole number of ounces. The problem is to place known weights in the pans to make the scales balance and so determine the weight of the object.

You have a large (infinite) supply of weights of two kinds, and you have to figure out how (or if it is possible) to place some of your weights on each side of the balance in order to correctly determine the object's weight.