There are a couple of things that could be happening here, but one thing that comes to mind is that maybe the stroke-width is not properly defined on the objects in the symbols.
Some attributes in SVG are inherited if not declared on the elements directly (just like in HTML/CSS, since there is a lot of overlap between those standards). Elements inside
<symbol>-definitions inherit the values of the
Make sure to explicitly set the stroke-width on the objects inside groups, not only on the group itself before converting it to a symbol. Inkscape usually sets properties recursively, but there could be situations where it doesn't.
Edit: After examining your files and some testing, it seems the problem is with the 'Display Units' in the document properties being set to 'mm' instead of 'px'. This may be a bug in Inkscape – I'd have to look into it some more to know for sure.
Anyway, try setting it to 'px' while importing your symbol. You can set it back to 'mm' after that. Also, maybe try only using 'px' units when making symbol sets.
There is also a duplicate symbol definition with the same id already in your second document, which will overwrite the symbol if you try to import it again. Delete all objects referencing the wrong symbol, then use 'File → Clean Up Document' to remove all unused definitions in the file before reinserting it.