I recently modified a cheap $5 string hammock to make it asymmetrical. The result was a substantial improvement in comfort and for negligible weight gain. There was one major problem (durability), but I'll deal with that in the second post of this thread.
First, I started with a basic, off the shelf all-polyester, woven mesh hammock that I bought in a camping store for about $5. The manufacturer said on the box that it weighs 5oz and it packs into a small ziplock sandwich bag.
It's comfortable enough when used normally, but I wanted to either add a spreader bar or make it asymmetrical to open it up a bit and make it a bit flatter.
Adding a spreader bar would require cutting the attachment rings and I already found it a little unstable and hard to get into, so it made sense to go asymmetrical.
I made it asymmetrical by making two six-point line groups in the HH asym side anchor positions. I rigged this from doubled waxed polyester #4 Marlow whipping line.
My first attempt used only one attachment point. This worked fine for a while and then eventually snapped when I got in in a clumsy manner one time.
My second attempt spread the load among six attachment points, more or less as below. Notice that the inner lines are shortest and the outer lines longer? That's because the hammock forms a corner at this area. I had to tailor the length of each line by finding the length that maintained equal tension on all lines.
Actually, it was slightly different to this picture. I tied off on only one line of polyester. I was sitting in the hammock and moved slightly, and there was a tack... tack... tack... tack sound. That was the sound of knots popping off one by one.
What had happened was I had applied a transient load from one side, over-stressing the outer hammock net knot, which failed and transferred the load to the next and the next, ripping each one in turn.
I temporarily solved the solution by tying off on two hammock lines. The added strength worked fine and there were no further failures.
I added an adjustable structural ridgeline and that took a bit more stress off the asym anchor points.