It sounds like some type of beetle. The larvae feed on the underside of the leaves sucking out the juice and the adults chew holes in the leaves. You don't say where you live, but you might want to take a sample of a twig with leaves attached in a sealed plastic bag to your local extension service.
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.