Charge by weight.
When the boarding agent takes your ticket, you step on a scale. A barcode or qr on the ticket is scanned and records your weight. Your credit card is adjusted from a national average. You weigh less, money is debited. Weigh more, credited.
Or better yet...
Using lasers, we measure a person's standing girth and calculate charges by the inch. It's easy to do. There's a grid of lasers on the x and z axis and what one blocks out is measured instaneously. Of course, people's girth are different on the y axis and we'll need a moving laser grid to scan for the optimal fatness.
When a passenger crosses a threshold of weight or girth, they are assigned two seats. If no seats are available, the cabin crew stands. We should all suffer equally.
Anyways, flying is already loathsome. Adding scales or lasers can make it moreso. But i'm not flying anymore so it is cool and the gang with me.
More Hassle and Less Privacy.™ TSA, you owe me on this!