Well, you could actually try and calculate it, but the first question is, "what is a rainbow?" Is a rainbow the water molecules in the air refracting the light, or is the light itself the rainbow? If the former, the weight would be the weight of all the rain drops in that portion of the sky. If the latter, the "mass" of the rainbow would be the mass-energy of all the photons flying through the sky at any given moment that are producing that image. Unbounded photons don't really have mass or weight. But if you trapped a bunch of them inside a perfectly reflective box, that box would actually weigh more.