Samuel,
My measurements are always by volume. I don't think barbecue charcoal of any kind will do the trick, activated biochar specifically is the best, but I use the black charcoal and ashes from a fire pit or my friends wood furnace because it's cheaper than buying biochar from a plant nursery, though that stuff is much nicer. The ash adds a super fine particle to the soil that I'm not thrilled by, so if I want to be careful about things I'll sift out the ash and crush the charcoal by hand as I mix it into the soil. The biochar you can buy at nurseries has no ash, and I think it's been boiled to "activate" it, not really sure on the science there, but I've used ash in a pinch and it didn't seem to hurt anything.
-Sol