Try to identify the offending herbage.,the more persistant ,ground elder, couch, nettles, marestail Creeping buttercup justify rigorous attention. The various grasses require just cutting before they seed. You cannot reasonably stray across your boundary but often a strip alongside the boundary could usefully be used as a path, and be mowed. If there is bindweed within it, cut along each side, with an edging iron, and mow. selective spot treatment of the persistant weeds with glysophate. Generally you shuld nt need to treat cultivated areas once tamed, unless you fail to cultivate. Organic methods: gas powered flame torches give good (and satisfying!) results, albeit quite expensive to run.
Once planted, the maintenance should be by hoeing or individual lifting with a hand fork. Do not become paranoid about weeds, often they are simply plants (maybe edible) in the "wrong place" Many excellent crops are harvested from plots containing weeds. Its all a matter of priority.