Tonnage is a type of tax. Tonnage is charged to the owners of ships that enter the United States, and the charge depends on how much their freight weighs.
See the word ton in tonnage? That’s a clue this word is related to weight. In fact, it has to do with how much cargo weight is on a ship that's entering the U.S. The greater the weight, the greater the tonnage, which is a tax the ship’s owners must pay. Companies that ship a lot of heavy, bulky goods to the U.S. have to pay a lot of tonnage.