Times carrying little message (5)
I believe the answer is:
tweet
'message' is the definition.
(type of online message)
'times carrying little' is the wordplay.
'times' becomes 'tt' (two abbreviations for time).
'carrying' means one lot of letters goes inside another.
'little' becomes 'wee' (similar in meaning).
'tt' enclosing 'wee' is 'TWEET'.
(Other definitions for tweet that I've seen before include "Small bird's chirp" , "throwaway message?" , "Short message posted on the internet" , "sound made by bird" , "Birdsong" .)