Unwilling to support son's laziness (5)
I believe the answer is:
sloth
'laziness' is the definition.
(sloth is a kind of laziness)
'unwilling to support son's' is the wordplay.
'unwilling' becomes 'loth' ('loth' can be similar in meaning to 'unwilling').
'to support' says to put letters next to each other (in a down clue, some letters hold others up).
'loth' put after 's' is 'SLOTH'.
(Other definitions for sloth that I've seen before include "Sluggish creature" , "tropical American native" , "Idle creature" , "Deadly sin - upside-down mammal" , "Idleness" .)