Weeping score by Big Apple (5)
I believe the answer is:
runny
'weeping' is the definition.
Both the definition and answer are adjectives. Perhaps there's an association between them I don't understand?
'score by big apple' is the wordplay.
'score' becomes 'run' (run is a kind of score).
'by big apple' becomes 'ny' (I am not sure about this - if you are sure you should believe this answer much more).
'run'+'ny'='RUNNY'
Can you help me to learn more?
(Other definitions for runny that I've seen before include "More liquid than usual" , "Inclined to be rather liquid" , "Fluid" , "(Of liquid) thin" , "Of liquid consistency" .)