If you have annual vetch mowing, hand pulling and a pre-emergent herbicide such as Amaze should give adequate control. It will likely take several seasons to exhaust the soil seed bank however. Here is a link that might be useful: How to Control the Vetch Weed

The root looks scary. Why don't you vegetation killer. The weed was sending me to the mental institution until I PUT MY HANFS on strazecide vegetation killer. The only ones I still pull by hands are those who decide to grow very close to the vegetable roots.

It could also be Nightshade, a relative of potatoes, tomatoes, and peppers. Sometimes where the plant roots into the ground can be difficult to see but by following the stem all the way down you can find it. Dodder usually has a violet, not a white, flower.

Got some other responses and I think it's a West Indian Nightshade (Solanum ptycanthum dunal). The description - including size - and pictures match perfectly. Yep, it's considered a noxious weed, but so are some other plants used in wildlife gardening. Reports of toxicity are varied but all seem to agree that a considerable amount of the berries and/or plant itself would have to be consumed to cause serious harm. I don't have to worry about children accidentally eating any of the berries, my yard is fenced and locked, and since the plant doesn't grow very large, I may try starting a few from seed since the mockingbirds appear to love the berries. Everything I plant is for the birds or butterflies; had to get rid of the grape vines since the only things eating the grapes were possums and my dogs. After relocating a litter of 7 "teenage" possums and realizing I would never keep my dogs and the grapes apart (grapes and raisins are very toxic to dogs), I reluctantly had my vines relocated to someone else's yard. Thanks again - if I see any Chinaberrys, now I'll know what they look like! Gretchen