It's possible of course, but it's a compromise between weight and screen size. Even a 17" laptop can be light, as the LG Gram 17 proves. Though it's not very rigid, from what I understand.
But if weight is your primary concern, it makes more sense to go for a small screen. If you go for a larger screen, you're already accepting a bit more weight. How much depends, but personally I'd expect a laptop that sacrifices weight for a larger screen to also sacrifice some weight to have a slightly better keyboard.
