Most people don't drive through DC, unless they want to see the sites in DC (memorials, museums, Capital, White House, etc.). If you're just passing through with no intent to go into the city, you'll likely be taking the Washington Beltway (I495) to I95 in VA. You can be sure that this route will be a nightmare during rush hour on M-F. On weekends, Sundays are lighter than Saturdays, but both days are typically pretty reasonable. I'd keep an eye out for accidents and construction prior to hitting these roads and consider alternate routes, if possible.
Taking route 301 is about 50 miles longer if you're coming south on I95... yes, it's much more tame, but on the weekend, I'd take the shorter route.
Greg