You cannot set the size of symbols in real-world units (meters, miles, etc). The size you specify is deemed to be in screen points. This is by design so that the symbols keep their size even when you zoom in/out of the map.
Hypothetically, if we allowed specifying size in real world units, would you expect symbols to disappear if you zoomed-out far enough. Say the line was 10 meters wide. At a sufficiently low map scale, the 10 meters would be less than a pixel wide and hence invisible.