Looks like it could be sheep's sorrel, Rumex acetosella. Sheep’s sorrel is a troublesome weed, because it can grow a tap root
down to a depth of almost two feet and the superficial
root system can extend 3 feet away from the shoot. In addition to this,
the roots develop bulbils from which new individuals arise. When you have one, you often have an entire wide spread colony.

The good news is that it is edible and is often included with salad greens, the leaves having a tart, lemony flavor.

Oh interesting. That's probably what it is because I definitely noticed that when I pull one up I need to not only go way down but often off to the side quite a bit. Hmm...maybe I'll be daring and taste one to confirm. Really quite annoying!!!

To me it looks vine-like and the leaves look the wrong shape for Sorrel or Sheep's Sorrel. Maybe Fallopia convolvulus, Black Bindweed, or a Convolvulus of some type. Can you post a clearer picture?

And please will you tell us where this is growing. It really helps.