Futurology

We lose thousands of tons of mass every year in the form of gases and gain a lesser amount in material from asteroids over the same period. The mass gain appears to have been quite dramatic, back when the earth was formed. Chaos would have reigned for a significant period after that, then we would likely have had a constantly diminishing amount of asteroid impacts. When exactly the earth went from a net annual gain of mass to a net loss is hard to say, but if you were to ask if the mass of the earth-moon system maintained an annual net zero mass change at any point, the answer would probably be "We don't know for sure."