Weight is the measure of mass in gravity,
Weight is lessened as its distance from the COG is increased,
or disappears if it is in free fall at or around a COG
Mass is a constant measure of a material composition, its (volume x atomic density) and so is not affected by gravity
Mass is what determines the needs of fuel and thrust in moving an object;
During launch there are additional secondary considerations, particularly from inside an atmosphere, namely escape velocity to create an orbit (always) and atmospheric drag;
But outside a gravity well or in orbit outside an atmosphere Mass is always directly proportional to Thrust and Velocity, increasing Mass requires more Thrust/Fuel to achieve the same Velocity in the same Time;
The same Velocity can be achieved by extending the Time and reducing Thrust, this ignores efficiency ratings which are largely what make this desirable in space (ion engines in particular)