FnHon offers the Freedom and the Tornado Mini Aluminium alloy framesets. These are 74|94mm OLD and can be equipped with Mialo wheels that come with a five-speed Sensah cogset (9-17t), RD and shifter for about $110. Yes, the whole enchilada for $110.
The framesets are meant for 14" wheels but most people use them with 16" (305) wheels with a limitation of 35mm max tire width, usually Kenda Ksmart tires. Chose your parts carefully and you can get them to 7kg quite easily.
TorMin
Freedom
Since these come with significant gearing, tire size and wheelbase limitations, you gotta make sure they are exactly what you need, a really light and tiny bike. For the same cost you could build yourself a far less limited FnHon Gust or Zephyr or Litepro Eno or Spyder 305 folder, for example.