Worries over small pet (6)
I believe the answer is:
caress
'pet' is the definition.
(I know that pet is a more specific form of the action caress)
'worries over small' is the wordplay.
'worries' becomes 'cares' (I've seen this before).
'over' is a charade indicator (letters next to each other) (in a down clue, some letters go over others).
'small' becomes 's' (abbreviation - e.g. clothes size).
'cares'+'s'='CARESS'
(Other definitions for caress that I've seen before include "Affectionate stroke" , "Scares with loving gesture" , "show of affection" , "Pat" , "pet[s]" .)