Most affectionate point about branch (7)
I believe the answer is:
warmest
'most affectionate' is the definition.
('warm' can be a synonym of 'affectionate')
'point about branch' is the wordplay.
'point' becomes 'west' (west is a kind of point).
'about' means one lot of letters goes inside another.
'branch' becomes 'arm' (synonyms).
'west' placed around 'arm' is 'WARMEST'.
(Other definitions for warmest that I've seen before include "Most affectionate, greetings perhaps" , "Most cordial or friendly, wishes say" , "most pleasant" , "Most hot" , "Closest" .)