how do shorter chainstays "transfer power more efficiently" - often hear this said, but I don't get the physics. (other than saving the weight of an inch or two of tube - or is it just that?)
I've read this before too, and wondered the same thing. I think (and I could be wrong) that longer stays are more likely to flex, so when the chain is under tension the whole BB to rear axle assembly will flex slightly and absorb some of the energy.
If I'm right then this will only happen under extreme torque/high chain tension situations. For normal spinny or relatively spinny riding there will be no difference. But for extreme Cav-like acceleration, or standing on the pedals on a hill like Contador after a nice steak, then it may come into play.
Not that it makes any difference to me personally, but I can't help thinking about these things.
Re the OP, bike weight is mainly significant going up hills. On the flat (once you've accelerated up to speed) rolling and air resistance are most significant.
Imagine you and your doppelganger are riding together, you on your bike, doppelganger on a new lighter bike. Your doppelganger will get to the top of some hills a wee bit quicker. But if you're riding within your limits you can just push a wee bit harder and catch up. At the end of the ride you will be a short distance behind your doppelganger or else you may be a wee bit more tired, but if you're not racing or riding to exhaustion this won't make much difference.
Or maybe you arrive together, but your doppelganger will have been able to linger over half-way coffee and cake for longer than you, or will have spent a bit longer having a wee or waiting at the lights.
So it depends what kind of riding you are doing: If you are racing and every second counts then it will be significant. If you are riding as far as your endurance allows, then you may be a bit earlier entering the "misery zone", when you are just churning the pedals and wishing for the end. But it's possible that a lighter bike may not be as comfortable, so you may enter the misery zone for different reasons.
There's also the fact that you may be grudgingly jealous of your doppelganger's shiny new light bike, and may not feel as good about yourself as a result. So the doppelganger, feeling happy aboard a nice toy, and getting to the tops of the hills first, may have a better time of it. We like toys, let's not pretend we don't. Also the light bike may have a racier "feel" to it, further enhancing your smug, hateful, doppelganger's mood and making you want to spit in his soup and never go cycling again.