It seems as though you are pressing ENTER twice in order to get
spacing between paragraphs. If you are, that is the cause of your
problem. Each time you press ENTER in Word you are in fact creating a
new paragraph. A blank paragraph will occupy a line of text, and will
therefore be counted by the Line Numbering feature.
What you need to do is to remove all empty paragraphs and specify
either Space Before or Space After for paragraphs to get the desired
spacing.
In order to get rid of the unneeded paragraphs, you can use
Edit>Replace. In the "Find what" box, type "^p^p"; and in the "Replace
with" box, type "^p". Then click "Replace All".
You can specify Space After in the Paragraph dialog box. From the
Format menu, choose Paragraph. Specify the desired Space After. A
value of 12 pt should be OK, but you can specify more, or less, if you
want to.