A quart of water weighs about 2 pounds. The exact weight of the water can vary based on its temperature, but 2 pounds per quart is a reasonable estimate for most common situations.
Another way to think about the weight of a quart is in relation to the weight of a gallon of water. A gallon of water weighs about 8 pounds at warmer temperatures. There are 4 quarts in each gallon. Therefore, each quart weighs about 2 pounds for a total of 8 pounds. It's important to note that a gallon actually weighs slightly over 8 pounds in many common situations, 8.3 on average, so a quart generally weighs just over 2 pounds.