It's been said that nobody can actually know how fast the Earth is moving through space, because a reference point is needed to determine absolute velocity. But if mass increases as speed increases, why can't this rule be used to figure out the absolute speed of anything?
The problem is that this mass change is also dependent on your frame of reference. The earth seems to stand still in our reference frame (more or less) which is why what we measure is actually its rest mass.
If you were to move in a spaceship at close to light speed away from earth the earth would appear more massive than to an individual that is standing on earth.
So as you see mass is also not absolute but proportional to an observers relative speed.