I experience the same problem with every file that I save as a .dwg. My "fix" is to open the drawing in AutoCad and change properties of the line (in my case I only have 1 line that I need to adjust so its not a big deal).
I also change the text styles to ROMANS. I have to run this command 2 times as the first time the command changes some SolidWorks text style to a True Type font that is noticeably darker than the other text.