Tilling soil has been one way to "kill" "weeds" for centuries and it can for a time do that. But tilling the soil also brings up new "weed" seeds that will grow and interfere with the more desireable plants you want to grow.

A better method of control is to apply mulch. If done properly mulches will aid in "weed" control, aid in soil moisture retention, Aid in controlling soil temperature, and eventually add needed organic matter to your soil.

Before the rototiller tilling was often done by hand with a hoe or other sharp instrument. If you have one use it to chop out the weeds if not a sharp butcher knife will work. After you have chopped them just below soil surface add the mulch Kimmser has suggested to keep them in control.

Got it! Perfect! It's the mulch that I was missing. :)

Thanks folks!