Meaning
Beyond feeling drowsy, in Patois 'sleepy' describes a person who is dull, slow, and not alert — one who misses what is going on around them and is easily caught out or taken advantage of. A 'sleepy' man is unsharp, behind the times, and half-asleep to the tricks and chances of the world, while 'nuh sleepy' warns you to stay awake and switched-on. So the word runs from the plain drowsiness of the tired to the sharper sense of the mentally slow and unwary, both sharing the idea of a mind not fully awake to what is happening.
Examples
-
Him too sleepy, everybody pass him by.
He's too slow/dull, everybody gets ahead of him.
-
Nuh sleepy, watch weh a gwaan.
Don't be dozy, watch what's going on.
-
Di sleepy one always get ketch out.
The unalert one always gets caught out.
Origin
From 'sleepy'; extended in Patois from 'drowsy' to 'dull/slow/unalert'.
How it’s used
Chiefly 'dull/slow/not alert', beyond just drowsy. Compare 'mumu', 'dibby-dibby'.