While the etymology of this word remains unknown, the OED sees it possibly as a variant of worsted n.. The MED adds ‘If the word is AF, its etymology in that language is a blank’.
s.
1textileosset, a kind of woven cloth, probably made of wool:
(
1346
)
Item consensum est quod instrumenta pro osetes faciendis decetero paciantur, ita quod stent in aulis et shopis juxta viam in conspectu populi
ii 4
(
s.xiv
)
Est ordeigné [...] qe [...] ne soient demurantz en la dite ville [...] fors .v. homes tanseulement usant le dit mestier de osetes
ii 41
osete (1346)