I choose to let most "weeds" grow, as if they were a cover crop, because in my climate having anything green putting roots into the ground is better than nothing. Before I make the decision to pull them out or let them be, I try to find all the information I can about whether that species has been utilized by anyone for food or some other useful purpose. In North America,
http://naeb.brit.org/ is an excellent resource for this sort of information.
But my gods, I really wish my local species/subspecies of lambsquarters tasted better than it does. I haven't tried cooking it yet, because cooked greens in general aren't really a part of my cooking repertoire. But compared to raw spinach or lettuce or kale, the raw lambsquarters has an unpleasant astringency that I just can't get over. I guess some people like that in their food, but it's not for me.
Like Thom said, I'm more interested in verified tasty plants that have the potential to survive without me babying them. For example this spring I have arugula that self-seeded and is growing like a weed, so I'm 100% going to lean into that and see how much free salad I can generate next spring.