We've been getting this weed growing on our property in recent years. It's one of the first weeds to sprout in the late winter or early spring (nothing else seems to sprout at that time but Creeping Charlie, some small unidentified weed, and this). It doesn't seem to mind shade. Someone I know claims that they're edible and delicious (but I want to verify what they are before I eat any of them, and I don't know if this person is right; I mention this in case it helps in a diagnosis). A flower can be seen in the third picture (there are other flowers, but they're kind of small to see in the other pictures). It seems to be an annual in my zone (I'm in southwestern Idaho). It's pretty easy to pull up. Usually, they haven't been this big, but I saw this nice healthy patch of them and decided to ask the question.
The last picture is of a single plant with its roots. That's about as big as they generally get in our garden. I don't recall if the summer heat kills them off, but they're more prevalent long before the last frost.
Upon questioning the person who claimed they were edible, the person thought they were cleavers (and tasted them and proclaimed that they tasted like cleavers, too). I don't think they look like the cleavers I see online, though.
EDIT: Here's a picture of the plants after they've matured more and gone to seed. Apparently, they turn into vine-like things with burr-like things on the nodes (which might be the fruit).
It seems like early in the spring, it grows vegatatively, but later, even the plants that aren't terribly old go to seed and vine around.