You need four weights: a one gram weight, a three gram weight, a nine gram weight, and a twenty-seven gram weight.
How it works: you measure a 1g stone with the 1g weight. To weigh out 2g, you place the 3g weight on the opposite end of the scales, then the 1g weight on the SAME side of the scales. 3g is easy to measure, so for 4g you combine the 1g and 3g weights on the opposite end, for 5g you place the 9g weight on the opposite end, then put the 1g and 4g weights on the same end, and so on down the chain.
To make this into an easy to swallow formula, the stone's weight must be equal to the total weight on the opposite side of the scales (let's call this B) minus the weights on the same side of the scales as the stone (C):
A = B - C