Rather weak dossier about newspaper (7)
I believe the answer is:
fragile
'rather weak' is the definition.
'fragile' can be an answer for 'weak' (I've seen this before). I'm unsure of the 'rather' bit.
'dossier about newspaper' is the wordplay.
'dossier' becomes 'file' (a dossier is a file or set of information).
'about' means one lot of letters goes inside another.
'newspaper' becomes 'rag' (informal term for a newspaper).
'file' enclosing 'rag' is 'FRAGILE'.
Can you help me to learn more?
(Other definitions for fragile that I've seen before include "To be handled with care" , "Easily broken or damaged" , "Breakable" , "Easily-damaged" , "Delicate, tenuous" .)