Why are landing fees at large airports based on weight?
From Anne Graham's book, Managing Airports:


  This charging mechanism uses the ‘ability to pay’ principles, since
  airlines using larger aircraft are in a better position to pay higher
  charges. Some costs such as runway wear and tear do increase with
  weight and also larger aircraft require vortex separations, which can
  reduce the number of aircraft movements during a certain period.
  Overall, however, there is not a strong relationship between aircraft
  weight and airfield cost. A flat rate landing charge for all aircraft
  types may be more appropriate, particularly at congested airports.
  This is because the cost of occupying the congested runway is movement
  related and independent of aircraft size. Each aircraft movement will
  consume the same resource.