Weeds, weeds, weeds

I am so sick of weeds. We, my neighbor and I, have a plot in the community garden in Woodbridge, Ct. So far, all we have really done is weed, weed, weed. What I really mean is pull, pull, pull. We are gardening organically so herbicides are a strict no no. Every day I weed for an hour or so if the weather permits. All we have is ragweed. Those roots are sooo much bigger than the plant above ground. It reminds me of spaghetti. I have to use a pick to dig the tangle of roots out! If one little piece of root stays in the ground, it grows more ragweed. I fantasize about those flame thrower weed killers and just toasting all of the roots... At least digging burns calories!