Pasting with different font sizes might be the expected behavior, depending on how your stylesheets are configured. In fact, it might not even paste with the same font family. Let's look at a simple example of why this might be.
Consider that you have two documents. Both of them use heading styles (eg: "Heading 1", etc). However, in one file your style "Heading 1" uses 14 point Tahoma, while in the other file that same style uses 18 point Garamond. If you copy a heading from the first document to the second, it will remain in the same style, but that style now enforces a different font/size (eg: the heading will switch from Tahoma to Garamond).
How this works depends on your preferences. The default behavior is that Nisus Writer will show you a style conflict dialog:

- conflict.png (47.93 KiB) Viewed 3973 times
What happens depends on the button you click. However, it's possible you disabled this warning in your General preferences. You'll want to look at the option "On Style Conflicts", near the bottom of the General preference pane.
Let me know if this explains the behavior you see. If not, perhaps it's related to your other problem with font sizes.