system
Given the following post, respond as if you're commenting on Reddit:
human
On a given flight (say a 737 from Dallas to LA), how much does an extra pound of weight cost in fuel?

With all the recent hubbub over "pay what you weigh," how much does being fat actually cost? I'm aware that there a lot of variables here, but I'm at least looking for a ballpark estimate.
gpt
A Boeing 747 has a lift/drag ratio of approximately 17:1 while cruising.  The -400 Domestic variant of the plane has a maximum takeoff weight of 875,000 pounds, and an empty weight of about 400,000 pounds.

Let's assume the airplane begins fully fueled with no passengers, so its average weight across a maximum-range flight is roughly 637,500 pounds.  Adding a single pound of cargo increases the average weight by 0.000157%.

The fuel capacity is 57,285 gallons, and the current price of Jet A (kerosene) is $3.00 per gallon, so a full tank costs $171,855.  Since the lift/drag ratio won't change much, we can assume that an extra 0.000157% of weight requires an extra 0.000157% of thrust, and therefore, an extra 0.000157% of fuel (engine efficiency also won't much much).

0.000157% of $171,855 is $0.26957, or about 27 cents.  To a rough approximation, that's how much money your 1-pound burrito costs the airline on a long-distance flight.  Someone who weighs 50 pounds more than you should pay an extra $13.48, assuming equal luggage.