Interesting question. Photons are sucked into Black Holes the way matter is so at some point they must become weighty when gravitational fields are immense otherwise they would not be pulled "down" towards the hole.
This post was edited by O-uknow at May 17, 2018 2:54 PM MDT
Photons have zero rest mass, but as they are never at rest they can be said to have relativistic mass (Einstein) - defined as Planck's constant divided by (lambda multiplied by the speed of light). This figure (which depends on the wavelength of the light) is so close to zero as makes almost no consequence, so it's not very heavy at all.