Wabi Lightning is a 17 lb steel fixed/singlespeed that sold for around $750-800 back in the day (EDIT as a frameset only) , now they're about 1300 (EDIT as a complete bike). If you can snag one used you can probably meet your weight and money requirements.
https://wabicycles.com/products/wabi...ng-se-frameset
https://wabicycles.com/products/wabi-lightning