I recall switching from a touring bike to a road (racing) bike years ago. The road bike was lighter and had a really short wheelbase. It accelerated much better and handled corners better. I also recall being in a short road race once and stripping the bike for the event - no frame pump, no rear pack with tools and tubes, no water bottle even. The loss of 3-4 lbs was noticeable.

So if you are reasonably fit and light, 2 lbs should be noticeable mainly in climbing, handling and acceleration. Also lighter bikes usually have higher end components, better shifting and better handling so that adds in too.

Now I recall, Diane nailed a friend of hers who had a new light bike by filling up the frame and handle bars with rice of all thing. He was at a light and the bar end was loose so he pulled it off and rice gushed out. He did not notice any difference by having a couple of extra lbs on rice on his high end bike. By the way, Diane is a mechanic so there was no damage.

The problem is that when we ride a bike with less weight we KNOW it. So it is hard to control for the placebo effect. That is the bike is lighter and therefore it will be better. It is hard to even figure a way to do it without going to some sort of outlandish lengths or having a bike mechanic friend with a warped sense of humor.