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georgir said:tl;dr
But the idea that something needs mass to be affected by gravity is obviously false - all things that have mass are affected absolutely identically by gravity, they receive exactly the same acceleration, regardless of their mass. So even if they had zero mass, it would be normal to assume they will still be affected in the same manner and get the same acceleration.
Do you mean that light can be accelerated overcoming its constant speed,or simply follows the space curvature? But curvating motion also means acceleration.