Airlines used to charge the same price for a seat for the whole season (perhaps three or four months) because everything was on paper and distributed around the world to thousands of agents. Then someone devised 'Yield Management'.
Having a per-seat price allows a starting point for price calculation, they then have these sorts of variables:
- Demand on the route
- Competition on the route
- Business / leisure demand on route
- Established route or new route (demand growing/steady/falling)
- Size of aircraft available to service route
- Cost of operating at the two airports
- Are there major events at destination: such as trade fairs or cities like NYC that always have demand
- If there is an F1 race that weekend - all seats into airports within a certain radius will go up for that event
- Is the destination a once-in-a-lifetime (Bucket List) such as Great Barrier Reef, Victoria Falls
- Season of the year at both ends
- etcetera
- All of these variables can be tweaked a dozen times a day or once a week - whatever they choose. They have departments whose only job is to price the seats at the right level.
They have enough variables to charge money that the weight of the pax is irrelevant. It would be a complication to add the weight at check in and then adjust the price of the ticket - what if the Pax then decides that it is then too expensive and not to go? You could have sold the seat to someone else.
Airlines review the average weight of passengers every year, I once participated in this. On an internal flight JNB-CPT, I was asked if I minded being weighed. I did not mind and the airline made some money by weighing thousands of pax and selling the information (along with the baggage weight) to other airlines.
The airlines all know that trying to charge extra to the oversized person (even if they overflow the sides of the seat) is one that will get them in court and scorched on social media. You can test this theory very easily.