The Collaborative International Dictionary of English v.0.48:

Weighage \Weigh"age\ (?; 48), n.
   A duty or toil paid for weighing merchandise. --Bouvier.
   [1913 Webster]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

WEIGHAGE, mer. law. In the English law it is a duty or toll paid for
weighing merchandise; it is called tronage, (q.v.) for weighing wool at the
king's beam, or pesage, for weighing other avoirdupois goods. 2 Chit. Com:
Law, 16.