The short answer to your question is if you are using wood for smoking or heat in your fire place they don't use weight because the volume of wood doesn't really change much with small changes in the moisture content. Now is you are using wood for flooring in your dining room then you need to take the small volume change with small changes in moisture content into consideration. You will need to leave a little room at the end points for wood expansion due to moisture changes. Still, when buying wood flooring or for construction you still buy it by "board foot" which is volume and not weight.
The long answer is that it depends on the specie of wood and the moisture content of the wood. For example hickory and oak will roughly [I use the term roughly here because the wood will swell to some degree] weigh around 35 to 60 pounds/cubic foot depending on the moisture content. Maple maybe 38 to 48 pounds/cubic foot. So, hickory at 0.00% moisture will come in at roughly the 35 pound range. At saturation [all air spaces filled with water] hickory will be around 60 pounds. That means that the water in the saturated wood weighs about 25 pounds which tells us that Hickory is roughly 42% pore space [25 divided by 62.5]. Most of the ground you walk on is about 50% pore space.
A cubic foot of water weighs 62.4 pounds at sea level. So, any cubic foot of wood that floats on water will weigh less than 62.4 pounds per cubic foot. Black Ironwood comes in at roughly 85 pounds/cubic foot so it will sink like a rock. There are lots of wood species that are more dense than water. My guess is that all of the woods we use for smoking will fall into the 25 to 60 pounds/cubic foot range. I use some alder and it will come in at the low range of about 25 pounds/cubic foot.