Not having had a drop in weight, facing chilly grave (5,4,5)
I believe the answer is:
stone cold sober
'not having had a drop' is the definition.
(not having had a drop of alcohol)
'in weight facing chilly grave' is the wordplay.
'in weight' becomes 'stone' (stone is a kind of weight. I am not sure about the 'in' bit.**).
'facing' means one lot of letters go next to another.
'chilly' becomes 'cold' (I've seen this before).
'grave' becomes 'sober' ('sober' can be a synonym of 'grave').
'stone'+'cold'+'sober'='STONE-COLD SOBER'
(Other definitions for stone cold sober that I've seen before include "on the wagon" , "off the booze" .)