Some delay in quoting the weight (4)
I believe the answer is:
wait
'some delay' is the definition.
(synonyms)
'quoting the weight' is the wordplay.
'quoting' shows a homophone (sound like) (I've seen 'quoted' mean this).
'weight' is a homophone of 'WAIT'.
'in' is the link.
(Other definitions for wait that I've seen before include "Linger, delay" , "singer" , "Cool one's heels" , "Watchman" , "Serve on tables" .)