I guess I'm mystified by the debate since anything in the aircraft, bag or no, has no bearing on the weight of the aircraft. The fact that the cabin and some of the cargo holds are pressurized makes no difference whatever. Everything in the aircraft (and, of course, the aircraft itself) is borne by the aircraft. If it weighed X pounds sitting on the end of the runway, it will weigh exactly the same in flight (other than the obvious loss of weight by the fuel burned @ 6.79 pounds per gallon). Old story about a flock of chickens in the back of a truck (excuse me... lorry)... would the truck weigh less if they all suddenly took flight? No... because they've simply tranferred their weight to the air which is still contained by the truck...
Jake's analogy is flawed by the same scenario... the buoyancy of which he speaks doesn't exist since... just as on the surface of the earth, the air pressure surrounding the bag exerts the same pressure on every square inch of the bag. Fact is, the air pressure on the surface of the earth (assuming sea level) is actually higher than the pressure inside of the aircraft, since at say Flight Level 350 (35,000 feet above sea level) the air pressure is equivalent to about 8,000 feet above sea level on earth...
This would remain true, even if the bag were a balloon filled with helium... the weight (let us simplify the discussion by not confusing mass with weight, OK?) is contained by the aircraft...