Let's say Chicago to New York is $.89 per pound each way (minimum charge, $100). You weigh 200 lbs. and your luggage is 100 lbs., your cost is $267. You want to save money, cut down on the luggage or ship it ahead UPS. Or go on a diet.
A 150 lb. woman with no luggage pays half that.
Place the scale at the ticket counter or gate, insert credit card, type in your code which identifies the rate you negotiated, and you're billed in total privacy (ie, your rate and weight are hidden).