Sighs audibly at the sheer magnitude (4)
I believe the answer is:
size
'the sheer magnitude' is the definition.
'size' can be an answer for 'magnitude' (size is a kind of magnitude). I am unsure of the 'the sheer' bit.
'sighs audibly' is the wordplay.
'audibly' shows a homophone (sound like).
'sighs' sounds like 'SIZE'.
'at' acts as a link.
Can you help me to learn more?
(Other definitions for size that I've seen before include "Magnitude; glue" , "mass" , "Physical magnitude" , "gelatinous mixture" , "Amount" .)