Quick Answer
Small cup measurements do not convert to one fixed gram value for every ingredient.
For example, 1/4 cup is about 31 grams of all-purpose flour, 50 grams of granulated sugar, and 57 grams of butter. A 1/2 cup is about 63 grams of flour, 100 grams of sugar, and 114 grams of butter.
The right grams answer depends on the ingredient because cups measure volume while grams measure weight.