In "The Canterbury Tales," what is the weaver's job and what does he wear?

The Weaver is not a he.  The Weaver was the Wife of Bath.  Weavers made clothes and The Wife of Bath was famous for her clothing.  Chaucer describes her as written below:

“Her head-dresses were of finest weave and ground; I dare swear that they weighed about ten pound Which, on a Sunday, she wore on her head. Her stockings were of the finest scarlet red, Tightly fastened, and her shoes were soft and new. Bold was her face, and fair, and red of hue. She'd been respectable throughout her life, Married in church, husbands she had five, Not counting other company in youth; But thereof there's no need to speak, in truth.Three times she'd travelled to Jerusalem; And many a foreign stream she'd had to stem; At Rome she'd been, and she'd been in Boulogne, In Spain at Santiago, and at Cologne. She could tell much of wandering by the way: Gap-toothed was she, it is the truth I say.Upon a pacing horse easily she sat,Wearing a large wimple, and over all a hat As broad as is a buckler or a targe; An overskirt was tucked around her buttocks large, And her feet spurred sharply under that. In company well could she laugh and chat. The remedies of love she knew, perchance, For of that art she'd learned the old, old dance.”