For historical reasons, and even in countries that otherwise use the metric system, weed is purchased using Imperial measurements; that is pounds, ounces and grams. A quarter of weed refers to one quarter of an ounce. An ounce weighs 28.34 grams so a quarter is just slightly over 7 grams.
Dried cannabis flower is measured and sold by weight and when you buy weed through a dispensary, an ounce is typically the largest amount that is available for sale. This is both a result of consumer preferences and state possession laws because most allow someone of legal age to possess one ounce for personal use. While growers and wholesale buyers (such as dispensary owners) work with weed by the pound, a consumer is unlikely to find more than an ounce available for sale in one package. So for the average cannabis consumer buying through a dispensary, a quarter refers to a quarter of an ounce of weed and not a quarter of a pound.
When buying marijuana the amounts sold are generally one gram (sometimes called a dime bag), an eighth of an ounce (3.5 grams), a quarter of an ounce (7 grams), half an ounce (14 grams) and an ounce (which is precisely 28.34 grams). A gram is enough to roll a good sized joint, pack several bowls for a bong and provides several sessions with a vaporizer. Such a small amount is often bought to check out a strain or for financial reasons. People often gravitate to the eighth as an ideal purchase amount; you can roll several joints, pack at least ten bong hits or create a good batch of cannabis infused butter with this amount and it ensures that the weed is consumed before it has time to lose its potency. Regular users, however, will gravitate to the higher amounts such as a quarter, half or full ounce.
The best way to ensure that you are actually getting your money’s worth when buying a quarter of weed is to use scales. Marijuana flowers can be deceptive when assessing their weight by eye. Some may have a large volume but a small weight and vice versa. In a dispensary they will weigh out your flowers on a scale in front of you so that you are assured of proper measure. If you don’t have a scale handy there are some smart phone apps that will give you an estimate based on a photo but, once again, the density of the flowers and the amounts of oil they contain are the determinants of weight and these can vary wildly for the same apparent volume.