I never pull weeds anymore. I use this hoe and just leave the weeds in the bed after they are cut. If your weed reproduces by an underground root system like bindweed it will not work so good, but I use it on them anyway in my ornamental garden. Once a week for 20 minutes keeps the garden looking good. This weeding hoe is the best invention ever.
you won't be breaking your back anymore!
http://www.johnnyseeds.com/catalog/subcategory.aspx?category=292&subcategory=634
If it is a bind weed like weed in your veggie garden I think mulching might be best. I don't know what that weed is you have there but if it comes from seed rather than spreading roots you shouldn't have a problem. Get a hoe like above.
I have read that chlorine dioxide kills bind weed and there are some products that have it.