Those look like native or wild mullberries to me. "Domesticated" mulberries are larger if I remember right and not so much stem--I picked some for a neighbor "on the halves" in his backyard when I was a teenager. afaik, I don't have any one my property but my sister has several, which never produced much, until the season after 2011's drought and they made berries in droves. Seems like everything did much better right after that drought. Lots and lots of muscadines too.