Garlic Mustard, Alliaria petiolata, is a food source for caterpillars of the Green-veined White and Orange-tipped butterflies, which lay their eggs on this plant in "untended" gardens.
The leaves are good to eat when added to a salad. Nettles also add "good stuff" to any vegetable soup.
So leave some "weeds", i.e. wild flowers, for your kitchen as well as for the butterflies that we all love to see....... except cabbage whites, perhaps!
Don't they look attractive against an otherwise boring fence? And they don't really compete with the Kiwi fruit growing up on wires.