Possible Clues:

• Times' first edition shows substance
• See 1 Down
• That's not a bit thick
• Sit back with girl needing one for a good cry
• Paper hanky
• A this sounds as if it's cold and makes one thin
• It's herself that's not a bit thick
• A little tea will make 30 down very thin
• Common purse item
• 'Thin, soft paper (6)'