Measurements are based on either weight, or volume (capacity).
A cup (volume measurement) of honey, for example, is pretty heavy.
It weighs 339 grams (roughly 12 ounces).
In contrast, a cup of popcorn weighs much less (8 grams, or roughly 3/10 ounce).
There is no specific conversion between weight and volume, because it depends on the density of the food item.
However, the density of water is often used as a standard to derive the weight of a volume specification.
One cup of water (at 4 °C) weighs 236.588 grams (roughly 8 ounces).
To find the density of an item, enter either part of the food description (e.g: corn starch), or it's USDA ndb_no (e.g: 11011):