Having just done a module on grassland management I hope I can help!
I think the most economic thing for you to do to begin with is find out what you are dealing with, ie perenial or annual. Annual weeds just need a top before they go to seed, and the next year the population should be greatly reduced. The perrenials, you have two methods of attack, you could keep topping them to deplete their reserves, and stop they going to seed. Or you could go for a chemical approach.
The most important message I guess is to top before going to seed, save yourself problems later on and in other areas.