Apparently the way to do this is to get a large bowl of water filled to the brim, and take note of how much water is in the bowl.
Take your shirt and bra off (dur) and place one of your breasts into the bowl so that the brim of the bowl is pressing against your chest.
When you take your boob out, the amount of water that was displaced is how much your boob weighs!
I learned this courtesy of Lolita_girl, so please, give credit where credit is due. She also recommends doing this in a place where you don't mind there being a lot of water, but of course that entirely depends on how large you breasts are.