So weight (or should I say mass) has nothing to do with flight?
Yes, because heavier weight = lower flight level (if close to optimum). Lower flight level normally means higher temperature. Higher temperature = higher TAS (if mach is the same), as MACH = TAS/LSS where LSS = 38.95 x sqr(temp in Kelvin). Many an aviator and controller seem to forget this, so even with the same wind, a heavy 747 at FL310 is faster than an empty one at FL 410, just for the sake of the temperature. Crossing the Pacific recently, we were playing with another 747, taking turns at passing each other as the winds were shifting in the different levels (he was 4000 feet above).
How big is this difference in TAS?
Mach .85 @ -56.5C: TAS = 487 (Could be FL410)
Mach .85 @ -46.4C: TAS = 499 (ISA for FL310)
OK, just 12 knots, but still :-) If the wind is the same ...