Consider a beam of sunlight falling on your skin; after a while your skin warms and, eventually, will burn: light carries energy (which is absorbed by your skin thus increasing its temperature). Recall also that a body with mass m, by its very existence, carries and energy m c2 (Sec. 6.2.8). There is no way, however, in which we can associate a mass with light; for example, we can always change the speed of a mass (even if only a little bit), but this cannot be done with light.
The force of gravity affects both light and all material bodies; since both carry energy, but only the bodies carry mass, it follows that gravity will affect anything carrying energy. This conclusion lies at the root of the construction of Einstein's equations which describe gravity.
Note that this conclusion has some rather strange consequences. Consider for example a satellite in orbit around the Earth, when the Sun shines on it it will increase its energy (it warms up), and gravity's pull with it. When the satellite is in darkness it will radiate heat, lose energy and the force of gravity on it will decrease .
Again let me emphasize that this argument is not intended to imply that light carries mass, but that gravity will affect anything that carries energy.