The Government Digital Service had a great blog post about typography in which they described this technique of normalising a website of typography so that you can critically evaluate if a different font style is actually needed.
If the page makes perfect sense normalised, there's little point in complicating it with multiple styles (imagine if a novel was printed that way). But if there's not a clear hierarchy and the content gets lost in the design (or lack thereof) then you can start to introduce different styles.
Drag me to your bookmarks bar and then click it to start using it on the site you're evaluating.
Notes: to try to catch as many styles in one swoop as I can, I'm using the '*' element selector, so this is really quite slow on some sites. Give it a few seconds as your browser re-renders the page with the revised style.