The majority of costs to the airline are in taxes, airport fees, and lease costs of the plane. I think you’ll be surprised to find out that fuel consumption is a very minor part of the ticket cost. You must also consider that the increased fuel consumption of +50kg of extra cargo to a system that is 100+ tons to begin with is going to be a bit negligible.
Sure you could have a progressive weight charge. But it’s gonna be more like $1 for someone who is twice your weight. Not twice the ticket price.
Welcome Chris! I have been to most of the national parks in the UK but I have not been to Northumberland yet. Thanks for sharing!