!!SCIENCE!!
So, in other words, de Broglie waves. Light has momentum and when it interacts with objects, there is an impulse force that pushes away the light, or specifically, the photons. That impulse force, through Newton's third law of motion, gives rise to a reaction force that acts on the object, which adds an "apparent mass" if the impulse force has a component in the opposite direction as gravity or reduces the "apparent mass" of the object if the impulse force component has the same direction.
Basically, it's like when you're in an elevator. When the impulse force is opposite gravity i.e. when you travel up, you feel heavier, and lighter when traveling down. Your inertial mass remains the same, but your apparent mass changes. Oh, the joy of non-inertial frames of references.
(Note though, that the analogy above is simplified, but the principle's the same.)
That said, it irks me when he says that Chicago has 140 kg more mass during the day due to sunlight. Technically, that's not true since no extra mass has been added (excluding pair production from gamma rays). It's only the additional reaction force that makes Chicago feel "heavier".
On the other hand, Chicago may actually, given a photon has enough energy, lose mass due to the photoelectric effect.
/rant
Speaking of de Broglie waves... You, the reader of this post, are currently emitting waves whether you like it or not. And you can't wash them away in the shower, either.