Just as violins have different sizes, bows do as well. A full size bow is the largest bow size and is usually between 57-63 grams. Here are the different sizes of bows/violins.
4/4 Size (Full size) – Normally a student about 12 years old
3/4 Size – 11-12 years old
1/2 Size – 9-11 years old
1/4 Size – 7-9 years old
1/8 Size – 5-7 years old
1/16 Size – 3-5 years old
A violin and bow should match respectively in size. There are also 1/10 and 1/32 size violins/bows but they are less common. As you go down the list, the bow and instrument get smaller (bow shrinks about 1-2 inches per smaller size). Also, you will find that the weight of the bow will decrease about 5-10 grams.