I spent a while at the local food cooperative this weekend looking for weeds. Not outside in the landscaping, but inside with the food and spices. If I seem skeptical about some of these, it's not because I'm trying to give the co-op, or the herbals industry, a hard time. I know that these species are traditional remedies or foods representing just about every continent. And since I have battled many of these species personally, in the field, I'm tempted to say go ahead and eat as much as you want. Nevertheless, some of these are amusing to me, while others seem odd or even downright risky. None of these are recommendations, because I don't know my homeopathy… I'm just interested in the weedy angle.
Well-known food weeds
I'll give chamomile, quinoa, and grain amaranth a pass here, even though some of their close relatives are bad actors. And, interestingly, the only weed-by-name on the shelf was dill-weed, which isn't a weed at all.
Surprise - it's Medicine
At one time or another, humans have tried to eat anything. As I look up these weeds, it appears that most have a legitimate history of traditional homeopathic usage. Many of them are described as diuretics, or as tonics for the liver or kidneys. Nowadays, herbals tend to say “XXX has been used to treat…” which I consider suspiciously noncommittal.
And from online sources: 
Finally, I want give a special shout-out to field bindweed (Convolvulus arvensis), sold online as a laxative. This is also one of the worst weeds in the world. In California, it is found in pretty much all agricultural settings and in urban landscapes. In addition to being a tenacious perennial vine, according to folklore,
- vipers make their nests under it
- if a young woman picks the flowers, the object of her affections will die
- if you pick the flowers there will be a thunderstorm