What about dividing the weights into three piles, two piles with 9 and one pile with 8
Place the two piles of 9 on the balance scale. Their is only two conditions that can take place 1. The scales are balanced which means the lighter one is in the pile of 8. or 2. The scales are unbalanced. Lets go with situation 2 and remove the lighter (higher side of scale) Now divided these 9 into three piles of three. This would be the second weighing place two piles on three on each side of the scale. If balanced then the lighter weight is in the remaing pile (as before the two conditions are a balance or an unbalance. If they are unbalanced then remove the lighter side and using the third measurement place one on each scale and locate the lighter one. If it were balanced on the second weighing then get the remaining three and place one on each side of the scale and locate the lighter with the third weighing.
Now for the earlier case no 1 after the first weighing. Take the eight from that third pile and divide them into a group of three, another group of three, and a group of two. For the second weighing place the two groups of three on the balance scale. This second weighing will either be balanced telling you the lighter weight is in the group of 2, if this is the case, then weigh those two for your third weighing and select the lighter, The case was unbalanced for the second weighing, remove the three from the lighter side, and place two of them on the scales (one each side) and select the lighter one from this final or third weighing.