A squint is a look that has eyes partially closed. How do you say one has those eyes? Looking up squint-eyed, it's defined as either crosseyed or walleyed. How do you say one has eyes that are naturally partially closed like that of Garfield's owner?
The OP might be hesitant for one of two reasons:
- Possible reader confusion of squint-eyed with the derogatory "slant-eyed"
- the example of Garfield's owner being the intended example isn't one of being squint-eyed at all, and the OP wants a different descriptor.
To resolve the first possibility, give a fuller description of the character initially — one that mentions eyes in a perpetual squint. Remember, though, that squinting involves more than just the eyes; it requires furrowing the forehead in towards the center of the face. The OP must decide whether that fits the person the OP is describing.
To resolve the second possibility, realize that the exaggerated eyelids of people in Garfield are just a visual stylistic device to reinforce the overall cartoonish quality, not something intended to be an actual physical characteristic. If real people had their eyelids covering half of their eyeball, you'd describe them as "heavy-lidded."