Does a metal roof weigh more than an asphalt roof?

That depends on how much asphalt used. Regardless, a corrugated metal roof won't be significantly heavier than asphalt roofing and might even end up being lighter.

Non-corrosive metal roofing will, however, definitely be more rugged, durable, and smell better, though it might be more susceptible to leaks if it's horizontal, improperly installed, or in high winds.