I would imagine you could use ultra thin rope for heavy loads. I worked at a bungy jump place once and we had members of the Canadian military come to our bridge to test some very thin paracord. The rope they used did not look like it would be able to hold them but it did. But this silk is obviously way stronger then what they had I could only imagine how thin it would be and have the same strength
Probably something like dyneema
Dyneema fishing line is kind of frightening to handle IMHO. It feels like it's just waiting to sink into your skin.
There are artificial fibers that are much stronger, and you can buy rope made from them.