Kluge says that it came from Middle Dutch "stoffe", which got it from Old French "estoffe", which had a sense of 'cloth, mesh, fabric (especially of silk)'. He says the word's "economic background" is the importation of silkworms and silk weaving from Byzantium ("where Justinian had brought them in 552 from the Orient") via Sicily and North Italy to France and Flanders, and that the "assumed" etymology of the word in Greek στυφειν can thus be "supported on grounds of cultural history".

https://en.wikipedia.org/wiki/History_of_silk#Spread_of_prod...

But other etymological dictionaries say that the origin of the Old French term is uncertain and may not come from Greek.