Brain Teaser: What is the optimum choice of weights for a balance?

I learned of this problem from my grandfather. A balance scale has four weights. By using both the left and right pans to place the weights, any weight from 1 gram to 40 grams can be achieved. How much do each of the weights weigh?

To get you started in your thinking: How many places are there for the location of each individual weight? Using this and taking into consideration that each arrangement shows up twice by swapping weights on left and right pans, show that there are exactly 40 distinct arrangements. This tells you that the sum of the weights must be 40.