It starts with a paradox - if light has no rest mass, how can it be affected by gravity? Gravity does not exert a force on massless objects.
The answer is that mass warps the fabric of spacetime around it. As the fabric is warped/bent by massive objects, light travels along these bends. This is why gravitational lensing occurs for example - distant galaxies warp spacetime, so light traveling around them gets bent back toward itself. We can use this to see distant objects in the cosmos that would otherwise be too faint to detect.
We don't feel the effect because it's very small, however we can detect it. Some atomic clocks are so incredibly sensitive that they can detect just a few meters' difference in altitude from the surface of the earth.
Additionally, time dilations due to height differences of less than one metre have been experimentally verified in the laboratory.[14]
https://en.wikipedia.org/wiki/Gravitational_time_dilation?useskin=vector