I'm a bit late to the party but I've just discovered a very simple way to debug which font your browser is using.
In the Chrome Web Inspector, go to the font stack in the CSS pane of the Elements Panel. Then, starting with the top of the stack, change the name of the font (I add random letters) while keeping an eye on the text in question. When you change the one in use you will see the text change font as it falls back to the next one in the stack.
I assume something similar is possible in most dev tools
Voilá