Seeding over weeds

I live in the transition zone in North Carolina.  My fescue lawn has been overtaken by weeds and now it is about 70-80% weeds.  I would like to overseed with a mixture of tall fescue and KBG.  Will this be a losing battle since the weeds have really taken a stronghold over the lawn?  I have about one acre that I would like to get going on an organic program.  I want to have at least a decent stand of grass for my kids to play on instead of the prickly mess it has become.  The soil is clay.

This isn't based on experience, but on principle I'm inclined to think that the 20-30% will have an easier time taking ground from weeds than seeds would.

What do you suppose tipped the balance in favor of weeds? If you can address that issue, overseeding might be appropriate afterward, but most of the cheap & lazy ways to fix such a thing take a while, and perhaps it will be more like 60-80% grass before seeds will have a really good environment to start life in.

I think what has tipped the balance in favor of the weeds has been general neglect.  At first not wanting to put any chemical crap on the lawn, but also not doing anything else other than mulching clippings back into lawn.  The lawn has not seen lime for at least 4 years.  With our acidic soil, could this be a large contributing factor.  We have very little if any topsoil and mostly clay.