I have the same problem at my house-a wildflower meadow with weeds that infiltrate. Here are several tactics I use for knocking out weedy invaders. First, I never let the weeds go to seed. If I see weeds flowering, I immediately grab my pruners and cut down the plants. I mow my meadow each fall to prevent any weeds I may have missed from setting seed. Second, I spray the worst weeds with glyphosate (Roundup) herbicide. Weeds have a tendency to grow in clumps, so I knock out entire batches of thistles, burdock, and nettles at a time. Third, I pull as many weeds as I can to keep plants from developing mature seeds. Following these steps will take some effort, but after two or three seasons you will see a dramatic population decline in weeds.