Weight isn't mass; weight is the force acting on something due to gravity. Gravity effects light, albeit only by a little, so in this sense light has a small but nonzero weight.
I don't believe that's a correct interpretation.
The reason light bends in the presence of gravity is that space time itself is curved, and light follows a "straight line" on that curved space time.
Given weight is defined as `W=mg`, and `m` is `0` for light, light can't have any weight. I think the question is itself incorrect: you can't weigh light because light is not something you can "stop" and put on a balance.
The fact that gravity appears to "attract" light is an illusion. Light only has what is called "relativistic mass" which has very little to do with how we normally think of mass and weight.
> the reason light bends in the presence of gravity ...
This is also why gravity bends the trajectories of massive particles, which also follow geodesics of the curved spacetime (in the absence of other forces).
