Old English net "open textile fabric tied or woven with a mesh for catching fish, birds, or wild animals alive; network; spider web," also figuratively, "moral or mental snare or trap," from Proto-Germanic *natjo- (source also of Old Saxon net, Old Frisian nette, Old Norse, Dutch net, Swedish nät, Old High German nezzi, German Netz, Gothic nati "net"), perhaps originally "something knotted," from PIE root *ned- "to bind, tie." But Boutkan says it has no clear IE etymology and implies it might be a substrate word.
From late Old English as "light, open woven fabric used as protection from annoying insects." From late 15c. as "light, open mesh bag for the hair."
"remaining after deductions," early 15c., from earlier sense of "trim, elegant, clean, neat" (c. 1300), from Old French net, nette "clean, pure, unadulterated," from Latin nitere "to shine, look bright, glitter" (see neat (adj.)). Meaning influenced by Italian netto "remaining after deductions." As a noun, "what remains after deductions," by 1910. The notion is "clear of anything extraneous."
Net profit is "what remains as the clear gain of any business adventure, after deducting the capital invested in the business, the expenses incurred in its management, and the losses sustained by its operation" [Century Dictionary]. Net weight is the weight of merchandise after allowance has been made for casks, bags, cases, or other containers.
early 15c., netten, "to capture in a net," from net (n.). Sense of "to make as a net" is by 1789. Related: Netted; netting.
"to gain as a net sum, produce as clear profit," 1758, from net (adj.). Related: Netted; netting.