Little obligation to support second love (7)
I believe the answer is:
sweetie
'love' is the definition.
(I've seen this before)
'little obligation to support second' is the wordplay.
'little' becomes 'wee' (similar in meaning).
'obligation' becomes 'tie' (I've seen this before).
'to support' means one lot of letters go next to another (in a down clue, some letters hold others up).
'second' becomes 's' (common abbreviation).
'wee'+'tie'='weetie'
'weetie' after 's' is 'SWEETIE'.
(Other definitions for sweetie that I've seen before include "treasure?" , "Term of endearment" , "dear" , "Maybe boyfriend" , "Darling" .)