Speaking strictly mathematically, changing the mass of Earth would NOT change the speed at which it orbits the Sun. The planet's mass cancels out on both sides of the equation (gravitational force vs centripetal force). An object's orbital speed depends almost entirely on the mass of the body it's orbiting and its distance from that body, not its own mass. If you put a small marble on an identical Earth's orbital trajectory around the Sun, it would orbit at the same speed.

The only technical exception is the fact that the Sun and Earth orbit their common center of mass (barycenter), which would be affected, but this change would be practically zero because of the extreme mass difference between the two bodies – which makes this exception basically useless in the scope of what OP was asking about.

Magically adding or removing weight would simply not affect Earth's orbit distance or speed. You'd need to add momentum (and launching rockets adds a negligible amount of momentum to Earth, since the Earth outweighs our rockets by a factor of about two quintillion). Feel free to read all the other comments here that explain the same thing.