The
mass remains constant (disregarding fuel use, bits falling off, bug and bird strikes etc
) The
weight is the force exerted by a mass as a result of gravity - and changes with altitude and geographic location.
Most people have problems in defining their frame of reference when looking at forces, especially in cases of acceleration. There are two techniques - using an accelerated frame of reference (and thus producing a 'balanced' equation by including the "imaginary" centrifugal force) or a static frame - in which the forces are out of balance, and the resultant force is providing the observed acceleration. In either case the weight is unaffected.