big, deep, great, heavy, huge
little, slight, small, soft
loud, quiet
audible, silent
There was an audible sigh of relief when the news came through that nobody was hurt.

inward
Nancy heaved an inward sigh but did as her son suggested.

exaggerated
long
exhausted, long-suffering, weary
defeated, resigned
wistful
His departure prompted a few wistful sighs and the odd tear from admirers.

annoyed, exasperated, frustrated, irritated (esp. AmE)
relieved
contented, satisfied
collective
The crowd breathed a collective sigh of relief.

breathe, give, heave, let out, release
I breathed a sigh of relief.

hold back, repress, stifle, suppress
hear

escape sb
A weary sigh escaped him.

come
A heavy sigh came from her mother.

on a sigh
She let out her breath on a sigh.

with a sigh
‘I suppose we'd better get back to work!’ he said with a heavy sigh.

sigh of
She gave a deep sigh of contentment.

a sigh of relief

deeply, heavily
She sighed heavily and sat down.

softly
audibly, loudly
inwardly
a little
contentedly, happily
She looked at her son and sighed happily.

dreamily
The girl watching him sighed dreamily.

dejectedly, sadly, wistfully
resignedly
wearily
He sighed wearily as he looked at the pile of work.

angrily, exasperatedly, impatiently

in
He sighed in exasperation.

with
We sighed with relief when the noise stopped.