Strong thin rope for kite
Kite string is a product. It is designed to be strong and light to enable kites to fly under optimum conditions. For ordinary kites, ordinary kite string is sufficient.
High performance kites (large lift capability, stunt/performing kites) require higher breaking strength while retaining light weight.
Spectra line is constructed of high density polyethylene and is quite light and strong. I have used 1 mm thick x 2 mm wide Spectra line which had a breaking strength of 700 pounds. Another feature of this type of line is that it has very low stretch.
In the case of multi-line stunt kites, it's critical to have the lines remain at a specific length in flight. Spectra does this well.
Spectra is a brand name and the product can be found under other names.