Collocations for hazy - adj.

be, look
The distant mountains looked hazy and mysterious.

become
remain

very
a little, rather, slightly
Generally, it will be rather hazy today, with some hill fog.

with
The summers were hazy with pollution.

be
become, get
remain

extremely, fairly, very, etc.
I have only a very hazy idea about how the economy works.

a little, slightly, etc.
My memory of that day is a little hazy now.

still
I'm still slightly hazy about the details of what happened.

about
I'm a little hazy about my family history.

Hazy is used with these nouns:
memory, mist, recollection, sky, sun, sunshine