quantum field theory - 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?

Answer

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.