Why does light bend due to gravity?

While it is true that photons have no mass, it is also true that we see light bend around sources with high mass due to gravity. This is not because the mass pulls on the photons directly, but instead because the mass warps the space-time through which the photons travel.

Can gravity manipulate light?

Yes, light is affected by gravity, but not in its speed. General Relativity (our best guess as to how the Universe works) gives two effects of gravity on light. It can bend light (which includes effects such as gravitational lensing), and it can change the energy of light.