Fat person sobbing? (7)
I believe the answer is:
blubber
This clue is a double definition.
'fat' is the first definition.
(I know that fat can be written as blubber)
'person sobbing?' is the second definition.
(someone who blubs)
(Other definitions for blubber that I've seen before include "Sob bitterly" , "Cry uncontrollably" , "source of oil" , "Break down" , "Fatty tissue of a whale" .)