As is usual for Sigma, an odd design... It's extremely small and light, although most L-mount lenses aren't! If you like the 45mm f2.8, it's almost certainly the lightest FF camera/lens combo around. It's actually lighter than most lens options on an X-T3 - with the 45mm f2.8, it's very close in weight to an X-T3 with one of the f2 primes, since the Sigma body is almost exactly 100g lighter, but the lens is around 70g heavier.
Just about any other lens currently available, however, puts it in the realm of the heavier options available - any of the DSLR-conversion Sigma lenses, either of the new lenses today other than the 45mm, or any of the current Panasonic lenses are heavier than Sony, Nikon or Canon equivalents by enough to make up for the light body.
To get the very light body weight, Sigma left off two essential items, though - a viewfinder and a grip. When I first saw the pictures, I thought it had a small finder off to the side, which would have been an interesting tradeoff - give up the big finder in the "prism" bump on most FF mirrorless for a smaller finder in the old "rangefinder" position and a weight savings. No, it's viewfinderless. An accessory electronic viewfinder will weigh something between 30 grams (the tiny one for the Sony RX1) and 150 grams (the Leica Visoflex). A grip will weigh something, too - although perhaps not much, depending on what it's made of and how it attaches.
There are a couple of other tradeoffs. It uses a "small" battery (similar to what Fuji and Sony use in APS-C mirrorless and Sony used to use on FF as well until the A9 and the III generation) - according to B+H specs, it has slightly less power than a Fuji NP-W126S, slightly more than a Sony FW-50. The small-battery FF Sonys had lousy battery life, and Sigma has not historically done terribly well at power management. It has a single SD card slot - neither a more durable XQD card nor dual slots.
Is this really a still camera in the conventional sense at all? By the time it's ready to shoot with a viewfinder and a grip, it's probably no lighter than a "small-battery" FF Sony, and only 100 grams lighter (at most) than a Z or a "big-battery" Sony, half of which is given back by the weight of a spare battery. The most likely place to attach the grip precludes using a strap, unless there's a strap lug on the grip...
Thom Hogan thinks that it's more of a video camera that's meant to be mounted to things. It has a bunch of tripod sockets - what if it's meant to go on a drone, a gimbal or other forms of rigging? It's not only smaller and lighter than Sony, Nikon and Canon options, it's also nearly symmetrical, making balance easier with no heavy big battery on one side. It would still need light lenses to do its job, but it might well be the most convenient way yet to get the ubiquitous Sony 24 MP BSI sensor into odd places...