In the Player's Handbook it states only that a waterskin costs 2 silver pieces, and a barrel 2 gold pieces. With some research I learned that a waterskin can hold 1/2 a gallon and a barrel can hold 40 gallons.
But how much does the water cost and weigh? Even if you find a place to buy water, the Player's Handbook doesn't state how much it costs per gallon. Nor does it says how much it weighs per gallon. I couldn't find the answer in the Player's Handbook and I'm not familiar with gallons and pounds.
Best Answer
What makes you think that a well or stream costs money to use, by default? The DM is able create any sort of water monopoly he likes, but in general streams, wells, and lakes are plentiful and unguarded. DnD has a history of heavily implying that while Ale costs money at an Inn, the water is free.
As for its weight. When it is not explicitly discussed, 5th edition DnD mechanics are assumed to emulate real-world mechanics, such as the density of molecules and the laws of physics. So Water weighs approximately 8 lbs per gallon. This works out very neatly with the stated weight of a full waterskin, which would then be 1 pound for the skin and 4 for the water.