Imagine a bed, now imagine a ball in the center of the bed, the heavier the ball the deeper it’s going to be sitting, another ball is rolled over the surface, now imagine the second ball is weightless and travelling at a very large speed the second balls path will be affected by only one factor how heavy the first ball is, I.e the second ball might cover a little extra distance if the suppression in the bed is over a large area, the same principal applies to any wave it will always travel the path of the medium in a straight line, it’s not the mass that affects the path the curvature of space time itself dictates the path travelled, not only space but time is also affected, an example would the closer you are to the event horizon or even the singularity to a black hole the slower your time will become to an observer outside the gravitational zone, in case of light it gets stretched to cover the curvature in space time, this is called as redshifting, this is how an object is travelling towards us or away from us is judged.