If it is solid shale then you’ll need to bring in 6″ of soil to cover the area before you can grow grass.  if it is just “shaley” soil then you could probably get grass to grow there if you choose the right blend.   I’d suggest our “Super Sandy” blend.  It is the best for not only sand but any difficult soil.  The tall fescues that makes up the blend can push roots 2″+ into even the worst soils.   Get the grass started and, once it is established, you can use a weed killer on the weeds this coming September.  HERE’S a link on how to start a lawn from seed.