18-35mm f1.8 sigma would like to have a word with you. Light and compact. The lens of choice for many videographers. Issues... slow focus, questionable build quality, no IS.
The Sigma 18-35 1.8 is very much one of the lenses I had in mind that doesn't meet your requirements.
810g isn't exactly light, and makes it one of the heaviest non-cine lenses for the APS-C/super 35 format. Anything heavier than in the same format is going to be things like the sigma 50-100 1.8 and Fuji's super-teles.
So with it is f/1.8, it isn't lightweight and doesn't have IS. While it is technically a zoom, it's only barely so- for photography there's not much you would use that for that you couldn't use a 24mm or 28mm just as easily. For video, the only time you'd need that lens over a prime or a zoom with a more typical speed are when you need a zooming shot, but not much of a zooming shot, AND need an aperture wider than f/2.8 AND aren't shooting at your export resolution, preventing you from zooming in post AND can afford the optical and mechanical compromises compared to other workflows. It's a very narrow use-case indeed, which explains why, despite being widely advocated by internet gear-heads for videography, doesn't sell in the numbers to justify claims that it's "the lens of choice for many videographers".
The compromises involved in very fast zooms mean that they just don't sell in the numbers that first-party manufacturers generally require to justify R&D and marketing costs. Canon was able to justify the 28-70 f/2- probably largely because of the marketing value of having such an absurd lens in the new ecosystem, more so than because it was going to be directly profitable. Angieneux was able to justify a couple- though I think the 24-290 f/2.5 might be discontinued, and the others are more fast for their zoom ratio than fast on objective terms- based on being able to charge a high enough price to justify only selling a handful to rental houses and that being about it.
If you really want a super 35 f/1.8 lens that's technically a zoom, buy one of the Sigmas, because even the other third-party lens manufacturers like Tamron and Rokinon, don't see much value in that space.