Reply To: style sheets not behaving consistently

Chris is correct you are using soft returns between many of your headers and body text.
It looks like you have been doing some manual formatting as the first 4 paragraphs have soft returns.
Change them all to normal paragraph returns then apply the Paragraph Styles.
If the text is as you show make the Header style to be followed by Body text and Body text followed by Header, select all the text and apply Header text and then next style and all the text will format correctly as shown.

You can use Find and Replace to change the soft returns.