For weekend travel any time of the year, fly nonstop from New York to Washington D.C. for $147 roundtrip on American or Delta. If you live near Capitol Hill and want to check out the Big Apple for a quick weekend, this fare also works from Washington D.C. to New York.
I found seats departing New York LGA on Friday, February 1, returning from Washington D.C. DCA on Sunday, February 3.
Other travel dates are also available for weekend travel throughout the year as long as you purchase a ticket at least 21-days in advance of travel and stay a Friday or Saturday night. You'll find the same fare from/to New York-Kennedy (JFK) and Washington-Dulles (IAD) as well.
The $147 roundtrip price is a Basic Economy fare which does not include advanced seat selection and upgrades or ticket changes are not allowed. If you don't like these restrictions, a Main Cabin Economy fare is $60 more roundtrip.
Need a room in D.C.? Here's what's available for the mentioned weekend dates on Hotelwatchdog.