Wife badly affected, just a bit (4)
I believe the answer is:
whit
'a bit' is the definition.
(I know that bit can be written as whit)
'wife badly affected' is the wordplay.
'wife' becomes 'w' (abbreviation).
'badly affected' becomes 'hit' (hit hard).
'w'+'hit'='WHIT'
'just' acts as a link.
(Other definitions for whit that I've seen before include "Festival week" , "Iota" , "The smallest amount" , "Pentecost (abbrev.)" , "A little" .)