They don’t. To quote Marco Arment: "Those metal parts are the hinges, subject to the most wear, that need to be most durable."
See also:
https://www.youtube.com/watch?v=r-CkZ71iz68
The zinc alloy in the knock-offs is weaker than stainless steel. But still much more durable than the plastic its hooked to. In either one the upper part of the hinge will break before the lower.
I don't think the metal is there to add weight, however. Seems to me to be so it looks shiny and has the appearance of being more substantial than it is. (Thus stainless steel which doesn't tarnish readily.) I think it does make a difference having metal on the shell of the ear cups because that's where your fingers touch. Over time painted plastic will fade and show smudges. The metal covering can be wiped clean and maintain its appearance longer. But everything else is plastic and will fade so a pyrrhic victory.
I've literally stomped on them, run them over with a chair, had the cable go into the chair wheels (repeatedly) and then pull them off my head forcibly when I got up without noticing it. They are still fine.
I did break the audio jack when my headphone DAC fell of the desk and hit jackfirst into the ground (it sometimes doesn't connect properly and has to be wrangled about) :(
Bottomline, to me they are an amazing purchase.