If subatomic particles pop into existence all the time, why don't I gain weight? Watching Discovery's first episode of the first season of Curiosity (entitled "Did God Create the Universe?" by Stephen Hawking), I heard this information:

[...] you enter a world where conjuring something out of nothing is possible (at least, for a short while). That's because at this scale particles, such as protons, behave according to the laws of nature we call "quantum mechanics", and they really can appear at random, stick around for a while, and then vanish again to reappear somewhere else.

... and this isn't the only time I've heard this. I imagine countless billions (trillions!) of particles popping into existence all the time in the smallest of spaces for the shortest periods of time.
If subatomic particles pop into existence all the time and in all locations, why doesn't the weight of my body (or anything) change?
 A: There is Einstein's famous formula
$$ E = m c^2$$
that governs the relationship between mass and energy. The subatomic particles (actually particle-antiparticle pairs) are created using energy that has already been there. The Energy from which they were created also has its weight (in fact, most of the proton's and neutron's mass is kinetic energy, not mass of their constituents) and this is exactly the same weight as the particle-antiparticle pair has.
A: This$^1$ has to do with the uncertainty relation for energy and time:
$$\Delta E \Delta t \approx \hbar$$
where $\hbar\sim10^{-15}\,\mathrm{eV\cdot s}$ is Dirac's constant (or Planck's constant divided by $2\pi$). This means conservation of energy can apparently be broken for very short time scales. The emphasis is on the very. A particle can therefore be created from the vacuum, as long as it disappears again within some time scale governed by the above approximate equality. This phenomenon is called a quantum fluctuation.
For example, if you wanted to create a proton (mass of approximately $10^9\,\mathrm{eV}$) in a vacuum, it would only be around for about
$$\frac{10^{-15}\,\mathrm{eV\cdot s}}{10^9\,\mathrm{eV}} = 10^{-24}\,\mathrm{s}$$
which is obviously not very long. And a proton has a negligible mass compared to your entire body.
Of course, if your body is around, it's likely not happening in a vacuum. So then Neuneck's answer is probably more appropriate. The particles are created using energy available in the environment. In this case however, there's no reason for them to necessarily disappear since there was no breaking of energy conservation. So although this is probably the situation more in tune with your question, it is most likely not the situation that is meant in the quote. (quantum fluctuations are more likely)

$^1$ In the vacuum of space at least, and I think that's what they're talking about in this particular quote. In presence of other matter, it is (or should be) more conceivable to people that it is possible to create particles using some energy from the matter in the environment. Though upon re-reading the quote, perhaps they're talking about quantumtunneling as well.
A: there is a listing of conservation  laws on wikipedia
http://en.wikipedia.org/wiki/Conservation_law
one of them is conservation of mass-energy which states that both the total mass and the total energy inside an isolated system remain constant over time, as seen by any single observer in a given inertial frame. the above link says this is an "exact law, or more precisely has never been shown to be violated"
hence, according to this the reason you dont gain weight is because the total mass-energy stays constant (except for these transient "noise" fluctuations which add up to zero), 
and it seems Hawking is misleading the public, by extrapolating conclusions from phenomena which has never been observed to add up to anything
