There is some confusion here. When you give the copy command a source name that is a symbolic link - the "big" file - the one the link refers to gets copied.

Code:

cp linkname newname

Does not create a second link, it goes to the source instead and copies that. So you get lots of data.

Why else would a command like vi linkname allow you to actually change a file? Links are not like some kinds of filesystem objects example: snapshots that simply contain delta data.

Short answer : use the ln command to "copy" a link.

Also note that symlinks never tell you that the original files does not exist - until you try to stat or open that file. You can symlink across filesystems, but it is fraught with problems if you are not careful. Your USB symlink copy could rapidly become pointless.