AutoCAD DWG to EPS format - Help needed!

I am creating a drawing in AutoCAD light (plans with different line thicknesses) and it needs to be exported into an eps to be used by a graphic designer who needs good quality print.

We have tried dropping the file into Illustrator and also a DWG to EPS converter but on both occasions it looses line thickness and has strange dots where lines meet.

Is there any way of getting a good quality EPS? Or is it simply not possible with the vector conversions which I am a little hazy on? PDF's were not good enough quality.

Many thanks for your help.