Every particle has mass. Even force carrying particles like photons have mass. And indeed they have no rest mass, but, they are never at rest, so they always have mass.
Photons fall under gravity.
Einstein's general theory of relativity predicted this factor of two. The gravitational force is carried by a particle known as a graviton. It has no rest mass. It has not been directly observed. It is a stable particle and does not decay i.e. it's half life is infinite.