Possible Clues:

• Thin stuff, reverse of rich, sort of cheese
• Returned heavy cheese cloth
• Fabric — a fat eft (anag)
• Thin fabric put around thick cheese
• Chunky rolls with cheese that's fine and crisp
• Man blowing top, Greek character delivering material
• Stout knocked back with cheese? That's the stuff!
• Grease spilt over cheese cloth
• American sweet almost made a hole round fabric
• Crisp, smooth fabric