If you mean burr in the usual "comes off the plant and sticks to clothing/animal fur" sense, that charming behavior tends to class them as weeds in the minds of anyone who isn't of the "but there's no such thing as a weed" camp. They don't look exactly like the tiny green (later brown) burrs (latin name unknown by me) that plague my yard and animals and socks, but they are similar in aspect. Remove and burn or remove and place in trash, digging out as much root as possible and trying to not lose too many of the burrs, which will add to the seeds that are probably already in your soil to make the next several years annoying. Also try to learn what they look like when smaller (before they fruit) so you can pull them out earlier next year.
Not burdock - that's pretty easy to spot/identify (and eventually easy to spot even the year before it flowers, since it's biennial.)
Might be Hackelia virginiana, aka beggarslice or stickseed. Also a biennial.