"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.