If the 4kb file happens to look half-transparent when it shows up on Windows and have a filename which looks like .regular.file (notice the dot in front of the name), then this is perfectly normal and is the result of the Mac transferring stuff to a Windows filesystem.
You can delete the dot-prefixed "duplicates" without any problems. All they do is contain metadata about custom file icon position and comments and such, which you won't be needing anyway.
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