String that doesn't stretch?

Your best option is not rope or wire, but a chain and sprocket. The sprocket goes where the pencil is, with the links in the chain supporting the weight. Flexible to go around the sprocket and not slip or stretch under strain. Think something like a plain ordinary bicycle chain only a smaller form factor. Chain drive does not slip or stretch significantly. A bigger example would be a motorcycle chain. Next best after the sprocket and chain would be a metal braided wire which would stretch much less that any other fiber. You might try locating stainless steel aircraft control cables. Aircraft cables are braided small diameter, extremely strong cables for their size, which also makes them quite expensive pound for pound. It is not uncommon to find a 1/8" aircraft cable capable of supporting 2000 pounds. These cables are what they use in movies to suspend things without the wire being visible. The wire is so small that at a distance or more than a few feet, you can not see the wire at all. The film and your eye simply do not have the resolution to show the width of the wire. The width of the wire is less than the width of a pixel, so it "disappears".