With the five weights 1, 2, 4, 8, 16, we can weigh all integer grams within 3 1. Because this is an integer power of 2, for example:

3= 1+2

5= 1+4

6=2+4

7+ 1+2+4

9= 1+8

……

12=4+8

……

3 1= 1+2+4+8+ 16