If what you call poke weed is what we call poke berry just digging up the root ball and breaking off any new shoots should discourage it. The OH had to dig very, very deep when he transplanted some so deep to get rid of it too. We have some in the front yard and love it for the birds it attracts. Not in the back since we have a berry eating dog and it's poisonous.
Phytolacca - Wikipedia, the free encyclopedia
ETA: It's not really a root "ball." It's a big, big, big, long tap root.
Pokeweed Penn State Extension