(if applicable to the rating of the freight)
is more of a "dimensional weight" thing, like where air cargo uses both dimensions and weight to rate the freight, and depending on the surface carrier that gets used to shuttle it around, that might be the way it's rated throughout. Most times with expedited trucking it's weight, but volume is the measurement once in a while (drums, totes). But since it's the weight (depending on dimensions) that determines the kind of truck the customer gets charged, even most "volume freight" usually uses weight as the determining factor for the rating.
The weight's supposed to be accurate, but when it's going on a truck or van based on a weight range, the accuracy of the weight isn't that big a deal (unless you are getting close to overweight, then it is). Just the same, if you have a 400 pound skid of something, according to the BOL, and you show up and deliver a 200 pound skid of something, there could be a problem, unless a piece count or something else verifies that it's all there. (This could be a problem, for example, if you have a refer truck and pick up a 400 pound hanging forequarter, and a few hours later deliver one that weighs 200 pounds. Burp.)