WordNet sense 1 (filaments from a web that was spun by a spider):

cobweb

WordNet sense 2 (so thin as to transmit light):

cobwebby, diaphanous, filmy, gauzy, see-through, sheer, transparent, vaporous, gauze-like, vapourous

WordNet sense 3 (characterized by unusual lightness and delicacy):

ethereal

WordNet sense 4 (exquisitely fine and subtle and pleasing; susceptible to injury):

delicate