Cry a little, softly (4)

I believe the answer is:

weep

'cry' is the definition.
('weep' can be a synonym of 'cry')

'a little softly' is the wordplay.
'a little' becomes 'wee' (I've seen this before).
'softly' becomes 'p' (**).
'wee'+'p'='WEEP'

(Other definitions for weep that I've seen before include "Greet" , "Sob - ooze" , "lament" , "pipe" , "Pee-pee" .)

I've seen this clue in the Evening Standard.

Want a hint initially instead of a full solution? Install my app