This was inspired by a thread on the AUGI forums and I didn't realize that visibility in Linked Files behaved this way.
When you link a Revit Project into your main host project, the visibility is by default set to By Host View. You can change this option to By Linked View or Custom. So far so good.
If your host and linked projects were started from the same template, you might not notice this issue, which is probably why I never came across this head-scratcher. When getting a project file from some other source outside your office, you stand a good chance that the line weights in each file are not the same as yours and/or other linked files.
When your link visibility is set to By Host View, Revit will use your host project's visibility settings to display the geometry in the linked file/s, together with other settings as shown below.
Notice that Object Styles will also be represented based on the Host file. But here lies the problem: what if the line thickness mapped to the line weights are not the same in each file? That's exactly when you notice the problem. For example in your host project, you might end up with walls showing with different line thicknesses, because Revit will use the line weight per the host file, yet it will still map the line thickness of the parent project file to it's geometry. So while your walls might rightly be using line weight 5 for their cut representation, your host project's geometry will display at 0.018" thick lines per the host's line weight settings, but if the linked project has line weight 5 mapped to a thickness of 0.2", then Revit will use that thickness for geometry residing in that linked (parent) file.
The solution is easy: Use Transfer Project Standards to copy the line weight settings from your host project to the links. I personally don't think Revit should behave this way. If I say I want settings to be By Host View, I would expect the line weight to line thickness mapping to also be honored. Maybe we need a new line item to the above list: Line Weights. You agree? Great, go file a wishlist item on AUGI!