I think instead of "weight" you mean "mass". "Weight" refers only to the measurment of matter in a gravatational field. But that's another issue.
The answer is "no" light (or photons) have no mass. Or as close to none that it isn't worth mentioning.
Remember, light is the fastest thing we know of. The closer any bit of matter gets to moving at the speed of light, the more massive (if it helps, think "heavier") it becomes. Eventually it becomes so massive that the engergy it would take to actually get it to move AT the speed of light is infinate. So any object with mass cannot move at the speed of light. Since light DOES move at the speed of light (duh) it can't have mass.
BUT...light does have energy. And Einstein says energy = mass. And that's true. If you took a great big sheet of aluminum foil a mile across and stuck in into space, all the photons (bits of light) coming from the sun would whack into the foil. Eventually all that whacking would start to make the foil move. Just like the wind blows a sail. In fact, this sort of aluminum foil gizmo is called a "solar sail". So light DOES have a sort of mass when it is moving.
But for the most part when you're talking about an object having mass, you're talking about it's mass when it is sitting still. This is called it's "rest mass". And sitting still (if it could sit still) light has zero mass.