According to this answer to Is Earth getting heavier or lighter?:
tl;dr: The Earth receives 40,000 tons of dust from space every year, but looses 95,000 tons of Hydrogen and 1,600 tons of Helium every year as well. After all additional effects are balanced, the Earth looses about 50,000 tons a year.
According to this answer to Does launching a device into orbit change earth's orbit?
As long as "what happens in GEO stays in GEO" and there's no mass lost to deep space, the Shuttle and the Earth will mostly orbit around their common center of mass.
When the Shuttle is moving (relative to Earth) in the prograde direction (Earth's motion around the Sun), the Earth will be moving slightly slower than it normally would, but a half-orbit later when the Shuttle is moving retrograde, the Earth will be moving slightly faster than it normally would.
When the Shuttle returns, to 1st order (and maybe 2nd order as well) the Earth will be in the same place it would be if the Shuttle had never taken off.
It's quite a bit like the Earth and Moon orbiting around their common barycenter, and it being pretty much the EM barycenter that moves in a nice elliptical orbit around the Sun, except that as @RussellBorogove points out very effectively, it's a quite a bit smaller effect than that.
So as long as the launched mass stays in orbit around the Earth, the Earth's orbit is essentially unaffected. If the spacecraft goes off into deep space, then there will be an extremely tiny change in the Earth's velocity (rather than due to its mass change) by conservation of momentum.
If the Earth loses mass by natural process isotropically, the orbit will be essentially unaffected. Of course the Earth and Sun orbit around their common center of mass, so if the Earth gets lighter it will have an extremely tiny second-order effect on the orbit, but that's nothing compared to the effect that the outer planets have on the Sun.