I get your struggle, In any case, a double stroller - read more about the do's and don't here - is never a very small, very light option - it is either a mid-weight or a heavy one. At least, it is so, if you want it to be at least a bit spacious and comfy for your babies.
My first thought of a light model for two babies is actually the Valco Baby brand. They produce reasonably light double strollers, either non-reversible Valco Snap Duo/Valco Snap Duo Trend or the reversible Valco Snap Ultra Duo. These would be the ones I would probably go for if I wanted a light double while something that is comfy enough for small babies as well as older toddlers.
Another thought is the Baby Monsters Kuki Twin or some of the Easy Twin line if that is available at your place as these are also OK in terms of weight. And, lastly, I would think of the Baby Jogger City Mini Double if you can lay your hands on that, light enough while good quality.
Another, different option would be the Bumprider Connect as these are super small buggies that can be connected if the size matters incredibly much to you.