Fine food, a weakness (8)
I believe the answer is:
delicacy
I believe this clue is a double definition.
'fine food' is the first definition.
'a weakness' is the second definition.
(delicacy is a kind of weakness)
(Other definitions for delicacy that I've seen before include "expensive food" , "Nice bit of food" , "Choice item of food" , "Tasty titbit" , "chef's special?" .)