I could see making a hammock chair using the same materials as an UL hammock, but with the suspension I don't see it being much less than 10oz. A hammock is just a rectangle of good quality ripstop nylon with hemmed sides and triple-stitched tunnels on the ends. Any experienced sewer could knock one out pretty quick. Add whoopie slings, toggles or carabiners, tree straps and go.
FYI, my Grand Trunk UL with whoopie slings, toggles and tree straps is a pound.
A Grand Trunk Nano7 is reported to be 7oz and it uses carabiners in the gathered ends– you still need adjustable straps, or whoopies and straps. I don't think much of them for overnight sleeping unless you are a small person, but it would be okay for naps and a seat.
If you used say, 1/3 the fabric of a full hammock, you would reduce the overall weight by a few ounces, but not much more.
The problem with an all-webbing or line seat would be the pressure points. Hammocks have a lot of surface area so you don't get the high pressure spots. You might be able to construct a seat from line line Amsteel Blue at near 4oz, but I doubt you would want to sit in it for long.
Note that many hammock chairs use a spreader at the top. It would be easy enough to create one that uses a trekking pole, although I think a spreader is more for single-point overhead suspension. Using typical hammock suspension, you should be able to spread the reduced fabric to about the same angles as a full hammock and the spreader wouldn't be needed.
