Flimsy stuff mostly rejected by one wanting firm material (6)
I believe the answer is:
calico
'material' is the definition.
(calico is a kind of material)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for calico that I've seen before include "Given material for dress" , "Coarse cloth with a bright print" , "Unbleached sixteen down cloth" , "Coarse printed cotton cloth" , "White cotton fabric" .)