Hazy means misty — or unclear in the memory. Something is not coming through sharply.
The weather sense is about fine particles in the air rather than water droplets, so a hazy afternoon is warm and slightly blurred while a foggy one is cold and thick. The memory sense is very common, and having a hazy recollection of an evening usually admits more than it says. The noun is haze, and heat haze is the shimmer over a road on a hot day.
Old English
haswiġ — grey; ashen; dusky
Middle English
*hasi
English, today
hazy
From earlier hawsey (1625), a nautical term of uncertain origin. Possibly from Middle English hasi, haswy, from Old English haswiġ (“grey; ashen; dusky”), from Old English hasu (“dusky; grey; ashen”), from Proto-Germanic haswaz (“grey”), from Proto-Indo-European ḱeh₂s- (“bright grey”). by surface analysis, haze + -y; although Modern English haze is more likely a back-formation of hazy.
Etymology from Wiktionary, CC BY-SA