Almost all U.S. LTL carriers use NMFC freight classes, although some are attempting to move to a dimensionally-based system.
It might be tempting to declare that your shipment is a lower freight class than it actually is in order to secure a lower price, however, carriers will re-classify your freight for accuracy and charge you a fee for having to do so.
Density is the relationship between weight and size. A ping pong ball, which is very little material surrounding a good amount of air, is low density. Bricks, which are heavy for their size, are high density. In LTL shipping, it is commonly measured in pounds per cubic foot.