If you can identify your weeds and know which are edible, you can eat them. I eat them every day. I've even imported weeds into my yard so I can harvest them regularly. It's amazing! They grow like weeds! Much cheaper than organic vegies from the store.
Many, such as dandelion, were brought to this country as vegetables, and then people decided that another vegetable was more fashionable so they forgot about it.
The best book I've seen on this topic is "Edible Wild Plants" by John Kallas. Excellent ID photos and procedures.
My most common ones to eat are dandelion, false dandelion, nipplewort, goose grass, sow thistle, spiny sow thistle, shotweed/bitter cress, marsh mallow (there are many, many mallows), and ones that have gone feral like Earth chestnut, scorzonera, leeks, campanula, Alexander's, and leaves of Oregon grape, Bay laurel, hawthorn, and goji.