Yep mixing it up is deffinitely the way to go. The thickness of the line also implies how heavy a shadow is, so like, if you think about your character as a collection of "forms" (IE, 3D objects) as opposed to "shapes" you can use the thickness of your lines to describe the shadows of those forms.
I get that that probably sounds complicated for a cartoon, and like maybe a bit backwards (It's a cartoon! Why would you want it to be more "realistic??) and that's fine. But if you wanna be serious about stuff it's worth it to study this sort of thing.
EDIT: Also @dawgofdawgness is super good at this sorta stuff, you should check out her comic for examples.
https://tapas.io/series/Left-overs