Sentimental weakness (4,4)
I believe the answer is:
soft spot
'sentimental weakness' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for soft spot that I've seen before include "Sentimental fondness" , "Emotional susceptibility" , "Sentimental affection" , "showing fondness" , "Affectionate weakness for (someone/something)" .)