Correct, Line width, does not matter.
Yes, Two lines in the same place will. You need to clean up your file by removing dupes.
There is no way for the software to know that you do not want the laser to cut twice. And this is something that some people could and do build into files at times.
Many programs have a option to do this. For example, in Rhino, I have a alias that says "! _SelDup _Delete"
This tells the program to select duplicates and delete them.
Not sure what software you are using, but do a search for “deleting duplicates” in the software that you are using.