Bellyful causes greedy person to lose weight (4)
I believe the answer is:
glut
'bellyful' is the definition.
(thesaurus)
'greedy person to lose weight' is the wordplay.
'greedy person' becomes 'glutton' (I've seen this before).
'to lose' suggests deleting specific letters.
'weight' becomes 'ton' (ton is a kind of weight).
'glutton' with 'ton' removed is 'GLUT'.
'causes' acts as a link.
(Other definitions for glut that I've seen before include "Excessive abundance" , "Flood" , "An excess of something so that prices fall" , "A surfeit as of crops" , "Oversupply, plethora" .)