Your plant is a begonia.* I'm not sure which one, but I suspect it's a rhizomatous begonia.* You can read the descriptions of the different types here.
I found your picture to be very small so I put it on my desktop and enlarged it.* For a better id you might want to ask at this board for the American Begonia Society.* Try and enlarge the picture if you can.* Post it in the 'General Growing Discussions.
I'd love to know what you find out.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.