If such an airline were socially acceptable, would this type of pricing make sense? Start by focusing only on the passenger. The fares proposed by the website were around $2.00 a lb per trip: so the difference between me and say a former offensive lineman (FOL) could be a couple hundred bucks. My guess is that the FOL will likely chose another airline, that does not charged based on weight. This is a classical case of price discrimination, that is charging two people different prices for the same product. Typically what happens in this situation is that the discriminating firm cannot hold onto a lower price for the preferred customer (light weights), since they lose all the expensive customers.
There are some differences here though. Perhaps light weight people like flying on airlines with other light weight people. As Daniel Hamermesh points out on the Freakonomics blog “Also, heavier people spill over onto their neighbors’ seats, generating negative externalities for the other passengers” It is possible they might pay a premium for knowing the other person will be light.
Those who know the airline industry realize that charging heavier passenger more does happen. Southwest Airlines famously charges customers of size for two tickets. Their FAQ actually strike a nice balance between sensitivity to size issues and economic concerns. My favorite Q&A is
“Why not make your seats wider or add a few wide seats on your aircraft?
Our ongoing goal is to operate a low-fare, low cost airline, and the costs of reconfiguring our fleet would be staggering and would ultimately reflect in the form of higher fares for our Customers. Purchasing two seats on Southwest Airlines is significantly less expensive than purchasing one first class seat on another airline. “