I misunderstood a bit - but still you should understand that overseeding seed into an established sod bed of weeds - does not work well - thats why I mentioned using roundup. If your plot is just thin - then overseeding can be at least wirth a try.

Sseeding and then mowing real tight - can work to some extent. You definitely have to mow though to have a fighting chance. Some people like to "frost seed" in Late winter - right on the snow. This is fairly common in pasture maintanence.

eg http://www.gov.on.ca/OMAFRA/english/...cts/98-071.htm

good luck