Sweet potatoes are great. I always grow them for the leaves. Yum! I'm not a fan of digging
roots crops out of the ground. I'm lazy so I don't bother with the roots unless I grow them in containers where I can harvest them by turning just the containers over.
Chayote grows like crazy, so only a few would have to be planted to cover a large area. I just don't know if they would actually smother weeds. I'd have to plant a lot of sweet potatoes to cover a large area, but it's on the list of possibilities.