A digger would just chop up the roots of perennial weeds which will then regrow a hundred-fold from the bits!
Depends what sort of weeds they are. Excluding light by laying carpet, heavy duty black plastic, or cardboard would stop annuals in their tracks and give you time to dig a section at a time. Personally I would dig out perennials and, when they dare to reappear, spray with glyphosate.