I don't worry to much about the weeds, with everything else I have to do the garden is last on the list.
You can use salt sprinkled on the base of the plant it goes into the root system and kills them off. For bind weed there are two ways of killing it that I know of, one with a chemical you have to paint on, so not good for cats and the other is to dig every tiny bit up or it regrows.
My current problem is Pimpernel being everywhere, but as the bumble bees love it, so I left it in place and ornamental grass which has grown to 4 ft in height even with me cutting it back regularly.