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.

It seems a similar question was asked in Astronomy Stack Exchange, and this short answer links to the BBC News article Who, What, Why: Is the Earth getting lighter? which answers this question.

There are factors that are causing Earth to both gain and lose mass over time, according to Dr Chris Smith, a medical microbiologist and broadcaster who tries to improve the public understanding of science.
Using some back-of-the-envelope-style calculations, Dr Smith, with help from physicist and Cambridge University colleague Dave Ansell, drew up a balance sheet of what's coming in, and what's going out. All figures are estimated.
By far the biggest contributor to the world's mass is the 40,000 tonnes of dust that is falling from space to Earth, says Dr Smith.

Surprisingly, General Relativistic effects of Global Warming is considered!

Nasa has calculated that the Earth is gaining energy due to rising temperatures. Dr Smith and his colleague Mr Ansell estimate this added energy increases the mass of Earth by a tiny amount - 160 tonnes.

Using $E=mc^2$ that works out to about $1.4 \times 10^{22}$ Joules/year or $4.6 \times 10^{14}$ Watts. That's about 3.6 Watts/meter^2 or about 0.3% of the total power coming from the Sun, so it does seem to be back-of-the-envelope-in-the ballpark correct!

But there is something else that is making the planet lose mass. Gases such as hydrogen are so light, they are escaping from the atmosphere.
&quot;Physicists have shown that the Earth is losing about three kilograms of hydrogen gas every second. It's about 95,000 tonnes of hydrogen that the planet is losing every year.
&quot;The other very light gas this is happening to is helium and there is much less of that around, so it's about 1,600 tonnes a year of helium that we lose.&quot;
So taking into account the gains and the losses, Dr Smith reckons the Earth is getting about 50,000 tonnes lighter a year, which is just less than half the gross weight of the Costa Concordia, the Italian cruise liner, that ran aground recently.