You need an additional rule:
RewriteEngine On
RewriteCond %{THE_REQUEST} /news\.php/\S+ [NC]
RewriteRule ^news\.php/(.+?)/?$ /$1/? [R=301,L]
RewriteCond $1 ^((news|health|tips|weight|P[0-9]{2,8})/) [NC]
RewriteRule ^(.+)$ /news.php/$1 [L]
EDIT: To add a trailing slash to all non-files:
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule [^/]$ %{REQUEST_URI}/ [L,R=301]