Thanks Ann!
Most of these weeds are annuals and once scraped off they will not regrow. The tough perennial weeds are things we don't tolerate in our garden so we don't have too many of them. I have a lot to say about that subject and we covered it in depth on podcast #54:
http://garden.org/ideas/view/d...
For you, cutting that stuff down and covering them with cardboard is your best bet. Then cover the cardboard with mulch and with some luck that should pretty well suppress those plants from coming back up.