Until the discovery of the missing mass of the universe, I too thought that light had a small amount of mass, due to the gravitational effects we can measure.
The presence of missing mass, (AKA dark matter)explains that what we were measuring was the gravitational effects of the matter that the light waves are traveling through, and it also goes a long way in describing what gravity is.
Consider that dark matter which comprises upwards of 90% or more of the total mass of the universe occupies what we have always classified as empty space. This means we and everything in the universe is moving through that dark matter. Gravity becomes differential inertia.
But this also raises a whole host of other unknowns, just like every other answer we have found.
LOL - The farther I go, the behinder I get.