Why is light affected by gravity if it has no mass?
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Don’t think of gravity as a force in this case, think of gravity more as a bending of space-time.
Imagine you’re an ant that can only walk in a straight line, and you’re on a sheet of paper. As you march forward, someone bends the piece of paper so it no longer lays flat. You can travel, from your perspective, exclusively straight, yet with the fold in the paper, you’re facing a different direction than if the paper hadn’t been folded. It’s the same idea with space and light, the light IS travelling straight, it’s that the space it’s travelling through isn’t.
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