Scrawny person’s very small daughter (4)
I believe the answer is:
weed
'scrawny person's' is the definition.
(weed can mean a scrawny person)
'very small daughter' is the wordplay.
'very small' becomes 'wee' ('wee' is a Scottish word for small).
'daughter' becomes 'd' (genealogical abbreviation).
'wee'+'d'='WEED'
(Other definitions for weed that I've seen before include "Intrusive plant; weak person" , "Hoe to remove it" , "Plant growing where it is not wanted" , "Ineffectual person" , "Plant growing in the wrong place!" .)