Here's an example of light affected by gravity from General Relativity.

In this example we have two women. One is situated in a room with a light and the other is outside the room observing it.

In this image the observer is watching the woman in the room and everything seems normal. There is one light on the wall opposite the woman, casting light into the room and allowing the observer to view the room.

But if the room with the woman was travelling downward at massive speeds because of a downward force (close to light), and this is the point in which the room passes by the observer (not travelling downward). To the woman inside the room, everything in the room appears normal. Light will hit all sides of the room the same as before. But to the observer the light will be curved in the travelling direction. The speed of light is always a constant, so for the woman in the room a photon of light will travel from light source straight across the room, but to the observer that same photon will have to curve as the room moves downward in order to reach that same point in the room.

This shows light being affected by gravity. Although light is the fastest attainable speed and the limit at which information & energy can travel, it is not instantaneous. Because the lightsource is part of the room it is affected by the same directional pull of the room. As the photons from the lightsource travel across the room, according to the observer they will curve as the room travels down, affected by gravity.