This weed is Alliaria petiolata, also known as garlic mustard. It is a non-native invasive species in natural habitats within the northeastern U.S. This means it often out-competes and replaces native plants in biodiverse stands, turning these habitats into near monocultures of garlic mustard. For this reason, it would be best if you did not let the plant produce seeds, so as to cut down on dispersal to new areas. The good news is it is edible, and was likely introduced to the U.S. from Europe for this purpose. It has a spicy/mustardy garlic flavor and can be used for seasoning or in salads. The form in your picture is the second year growth. This plant is a biennial and grows as a low rosette during the first year, then over-winters and comes up with a flowering shoot the second year. After producing seeds the plant dies.

Here is a site with some more information:
http://www.nps.gov/plants/alien/pubs/...