Weight of air in 747 cabin
I was intrigued by this, so I ran some numbers through excel.
At sea level, temperature 27 deg C (300K), density of air is 1.18kg/m3 so with a cabin volume of 885.9m3 the mass is 1042kg. The weight of this air is balanced by the weight of air it displaces (Archimedes) which means that there is no effect on the overall weight of the plane. It is however an extra ton of mass that has to be accelerated to take-off speed, over and above what the aircraft would weigh on a weighbridge.
At 2000m, the air density is 1.006kg/m3 and the mass of a cabinful of the outside air falls to 891kg. The air temperature at this altitude is 2 degrees C, so assuming the cabin is heated to 300K and at the same pressure, the air inside is less dense than that outside. In fact its mass is only 817kg, so the aircraft is actually 74kg lighter at this point.
At 10000m, the density falls to 0.417kg/m3 and the OAT is -50 deg.C. The air displaced weighs only 365kg, the pressurised air inside (2000m, 27 deg.C) still weighs 817kg. Although the weight of air in the cabin is less than at sea level, the air displaced weighs even less. So the wings have to produce an additional 452kg of lift - nearly half a ton - to keep all that air in the air, so to speak.
I hope the beancounters at a certain low-cost airline aren't reading this...