I am afraid Illustrator can not split 'parts that could be a line' from 'parts that needs to be traced around'. Streamline did have that option, but that also was an 'on' of 'off' option. So that would mean you have to draw the thick lines that you want to vary with by hand. But still, you can also add thickness to the 'traced around'-version Live Trace makes. When you need to 'shrink' a line, you can add a white outline. Hope this helps! Good luck!