Beside the definitions Webster1913 gives, squint also means 'to look or peer with eyes partly closed'. Specifically, squinting means you have the muscles around your eyes tensed, to narrow them to a slit (as if looking at a bright light). If your eyelids are simply relaxed and drooping, you are either sleepy-eyed or a victim of ptosis.
In my experience this is the most commonly used definition; it seems to be used in both the US and the UK. I was rather surprised to find that Webster1913 does not also give the only definition of squint that I have ever used...
Gritchka reports that the Oxford English Dictionary gives the 'nearly closed eyes' definition as originating at almost the same time (circa the 1600s) as the one Webster1913 gives. If you have any more information about this word, please /msg me.
I have found one other definition for squint that Webster1913 doesn't give:
"An inclination towards some object, course, or procedure. TREND, BENT".