Let’s take it step by step:

1) Put three weights on each side of the balance.

2) If they are the same weight, you know that one of the remaining weights is the light one. Put them on the balance, one on each side, and you’ll have your answer.

3) If one group of three weights is lighter than the other, you know the light weight has to be one of those three. Take two of those three weights and put them on the balance, one on each side. If one is lighter than the other, then that’s your answer. If the two weights are equal, then the third weight must be the light one.