Small-minded? Afraid so! (6)
I believe the answer is:
scared
'afraid so' is the definition.
(scared means afraid)
'small-minded?' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'minded?' becomes 'cared'.
's'+'cared'='SCARED'
(Other definitions for scared that I've seen before include "in fright" , "Frightened, alarmed" , "Nervous" , "Afraid, anxious" , "Thing which precipitates an event" .)