Heaviness of the wig, perhaps? (6)
I believe the answer is:
weight
'heaviness' is the definition.
(how much something weighs)
'the wig perhaps?' is the wordplay.
'perhaps?' is an anagram indicator (I've seen 'perhaps' mean this).
'the'+'wig'='thewig'
'thewig' anagrammed gives 'WEIGHT'.
'of' acts as a link.
(Other definitions for weight that I've seen before include "Pressure" , "Avoir-du-pois" , "Trouble" , "Heavy load - preponderance" , "Something to lose" .)