Pedal weight and performance
I was answering the Physics.se version of this question but it got closed (probably rightly so), so I'm posting it here.



The lighter pedals will have very little effect on the performance of your bike, other than through the overall weight, and particularly if you're pedalling at a steady cadence instead of accelerating and decelerating repeatedly. 

Making any part of the bike lighter means that accelerating will be easier as you have less inertia, and that you will spend less power at any given constant speed, through a decrease in rolling resistance (i.e. you spend less work flexing your tires). However, you could achieve a similar effect by simply using a lighter frame or handlebars or haircut. To optimize this, if you really are in a trim-all-the-weight-possible mood, you should be comparing this to all comparable weight savings across your bike.

The only real property of the pedals that is affected is their moment of inertia. This means that heavier pedals have more energy stored in their rotational motion than lighter ones. The thing, though, is that at a steady cadence this energy stays constant and you do not need to worry about it. It only comes into play when you are accelerating, and frankly I would be more worried about your translational energy than the rotational energy in the tires and pedals. 

In a similar spirit to the above, if you want to minimize this effect, you should compare this with the moment of inertia savings on your pedals, wheels and tires. Since the rims have a larger rotation radius, and rotate at a much faster angular velocity, they hold far more rotational energy than the pedals, and any savings in this area are likely to be easier by using lighter rims.

You asked for math, but I'm afraid it's a bit pointless to do it. The reason is that one can in principle calculate how much energy you save in a given situation, but that will give you a number that doesn't mean much. The only way to give it meaning is to compare it with similar weight losses in your frame and in your rims, at the very least, where 'similar' must be understood, in fairness, to mean a similar increase in price. But then you're in a completely different ball game, far broader than what is in your question.