Remove weeds from the gr?

Rent a verticutter at your local equipment rental yard- $50-$75/day. Once set to the correct depth, run this machine across your lawn. Most moss will be pulled up giving the gr (and roots) much needed oxygen. As fas the weeds go, you don't have alot of non-chemical options- broadleaf herbicides can be used (judiciously) in order to control some of the weeds, however, don't overuse as the above info is correct in that it will end up in the water supply if used differently than what the product label recommends.