If you have vector art with paths ('paths' are what Illustrator calls 'lines') and you try to scale the image down to a smaller size, you'll find that the paths may not scale proportionally. While there are settings in the Preferences to avoid this, the end-all solution is to Outline the Stroke feature in Adobe Illustrator. This changes the line path to a shape instead, so it will scale perfectly in any application.
Here is how you can scale your vector paths/lines perfectly:
For a solution to the line scaling (path) & viewing issue in vector art, apply the Outline Stroke to your path/lines in Adobe Illustrator, then they will resize proportionally and appear perfectly.
To do this, select the paths to outline, then find under the main menu:
Object > Path > Outline Stroke
Alternatively, as you are designing, you may want to keep the paths while you design until you have the art approved. In this case, I change my Illustrator Preferences to "Scale Strokes & Effects" so when I resize, it retains them as a line and keeps their size proportional when scaling. This allows me to continue to adjust the width of the line path while designing. I always use Outline Stroke before sending art or logo vector files to my clients, as this will allow the line path strokes to rescale in proportion no matter what which or how their software preferences are setup.
Find this preference under:
Illustrator > Preferences > General > Scale Strokes & Effects (turn it on)