Simple Simon's core worry, being pushover (4,4)
I believe the answer is:
easy meat
'being pushover' is the definition.
'simple simon's core worry' is the wordplay.
'simple' becomes 'easy' ('easy' is associated in meaning with 'simple').
'core' means to look at the middle letters.
'worry' becomes 'eat' (eating is a kind of worrying).
The central letter of 'simon' is 'm'.
'easy'+'m'+'eat'='EASY MEAT'
(Other definitions for easy meat that I've seen before include "One's readily overcome" , "targeted victim?" , "a mark" , "No challenge" , "Sitting target" .)