I definitely should not jump in, but tytalan, you are wrong, and Sigtrygg is right. I will have a go at trying to explain what Sigtrygg means and we will see if my explanation gets across any better.
Mass is a property of all matter, and it does not change due to gravity. Weight is mass x gravity, but it is better to disregard weight for this discussion. If you fly your 1000 ton spacecraft to a 2G planet, suddenly it weighs 2000 tons, but the mass is still 1000 tons. Since it is variable in this context, hereinafter, I am not using the concept of weight.
Mass is what matters for determining, for example, how much force a spacecraft will need to exert to accelerate a given amount, and this is the case even in zero gravity. Even if there is no gravity, objects with more mass will require more force to accelerate than objects with less mass. So a 1 G M drive on a 1000 ton (mass) spacecraft becomes a .5 G M drive on a 2000 ton (mass) spacecraft (tons meaning tons of mass). This is because mass has inertia: force is required to overcome this inertia and the amount of force is proportional to the mass of the object, and this is the case both inside and outside a gravity field.
(This is confusing because experientially we only have ever to deal with objects in a 1G gravity field - usually they ARE "harder" to move in gravity except of course downward when it is easier)
If you have a gravity control based engine, it does not affect or remove objects' mass. Rather, it affects the effect of gravity on the objects - if you have a grav sled, with massive objects stacked on it, you can push it more easily because 1) gravity is not creating friction with the ground 2) you can accelerate the mass little by little instead of needing to continually overcome gravity with constant pushing. The mass is still there, though. If you get your massive sled going fast and it runs into something, all that inertia is still there.
In addition to nullifying the effect of gravity on the spacecraft, the Traveller M drive engines provide thrust, which we know because the rulebooks tell us so, and because it is measured in G forces, which is a measure of thrust. The mass of the spacecraft would be important for this reason, and technically the weight of the cargo in the ships should definitely affect the ships' performance if we want to be realistic. A cargo of cottonballs with the same volume as a cargo of gold bricks could both fit in the hold but one MASSES more that the other, and physics tells us this will affect ship performance - not in terms of ability to take off, since we can nullify gravity - but in the ship's G rating certainly.
This way lies madness, however, so we handwave the issue and just leave that can of worms tightly shut when playing the game.