If there were, everyone here who spent into the four digits getting their new bikes to that level would probably feel quite silly.
AFAIK, short of Bikes Direct or Wal-Mart, you'd have a hard time finding anything even with drop bars for $300 new.
That said, my "lightweight" Peugeot comes in around 24#, and my Schwinn nearly 10# heavier than that. For the riding I do, and the riding I suspect you would do with such a question, I actually find myself on the heavier bike far more often than caring about the weight savings.