Lie heavily on stone, at first? This is breaking now (4,5)
I believe the answer is:
stop press
'this is breaking now' is the definition.
(both might be said about breaking news)
'lie heavily on stone at first?' is the wordplay.
'lie heavily on' becomes 'oppress' (oppress can mean to press down on).
'stone' becomes 'st'.
'at first?' is a charade indicator (letters next to each other).
'oppress' put after 'st' is 'STOP-PRESS'.
(Other definitions for stop press that I've seen before include "Late news item(s)" , "breaking intelligence" , "Latest news" , "The way to be tyrannical" , "Late breaking news" .)