all of my responses relate to the Evocurve (not the item pictured in the OP, that's the Evolution i believe, which has a deeper drop).
What more can I say ... they aren't very WW I'm afraid. IIRC c.250g for carbon and about 25g more for alu.
They are ~200grams for the Carbon versions and 250g for WCS aluminum (triple butted) & 280g for the Pro (double butted)
But you bring up an alternative explanation: they sweep them that way to make them look like mountain-bike bars.
whaaa? i can't think of any motivation to capture consumers via this specific association.
think about the shape of a gun handle... specifically the angle between the handle and the barrel... can you see it in your mind? good. now, try this experiment:
when you hold a stick (or bar), wrist straight, the stick angles forward. when you rotate your wrist (as if on the tops of a drop bar) the stick (or bar) is still angled forward (perhaps slightly less-so). this curve allows your wrist to be a /little/ bit more straight and (i think) is designed to mitigate some wrist strain.
i'm always looking for bars with a bit of sweep back because my left wrist is pretty jacked up.
i just got some WCS'... I'll let you know how they work.