You could try making all the weed seeds germinate this year. It's late enough so that unless they're perennials or cold-tolerant annuals (or have a very short life-cycle), they should die with the cold without reseeding again (after they germinate this year, that is). If enough of them sprout this year, you may not have a problem next year (that's the hope, anyway). I don't know what kind of weeds you're dealing with; so, this may not be a viable solution.
To get them to sprout, you could water it pretty well for about a week. That by itself should get a lot of them to sprout, but if you want higher germination rates to ensure you don't miss as many for next year, you could add some food grade hydrogen peroxide (not the regular kind, since it can contain harmful stabilizers such as organophosphates and/or heavy metals; you can contact the manufacturer to see what they add) to the water or electrify the ground (both of which are said to help bring seeds out of dormancy, whether or not it's true); I'm not sure how effective they are at doing this, however. If you use too much peroxide (and/or electricity) and kill the seeds, I guess that won't hurt matters. The hydrogen peroxide should turn into water eventually. It would probably be safe to use the extra-potent food grade kind, if you wanted to.
Anyway, I don't know if this solution will help at all. It's just an untried random thought (granted, I'm in the process of trying the water only method, but as we're having an awesomely late frost this year, maybe I better just pull the weeds up, and that might be a good idea anyway, since they might be perennials).