AHD4 doesn't take them back any farther than OE, but

Weed (the undesired plant) is from weod:
http://www.bartleby.com/61/82/W0078200.html

Woad (the dye producing plant) is from wad
http://www.bartleby.com/61/79/W0197900.html

And, as a special bonus, weed (the clothing worn while mourning, as in "widow's weeds") is from węd
http://www.bartleby.com/61/83/W0078300.html