Why Large Disc at front and Smaller at Rear ?

Why Large Disc at front and Smaller at Rear?

As the car brakes, the center of gravity causes a torque (like a big wrench turning the car toward its nose) to force the car to its front tires.

The center of gravity of the car wants to keep going forward. The only thing slowing it down is the transfer of force between the road, and the contact patch of the tire on the road.
That force, which the tire makes with the road, is very simplistic...  That force is composed of only two things. The weight pushing down on the tire, and some number that makes up for the stickiness of the tire, and the terrain it is on.  A sticky tire on good pavement, a high number; a normal tire on ice, a low number.

Since that force on the tire is highly dependent on the weight on that tire, the amount of braking that the tire can do is directly related to the weight imparted on the tire.

As you can see from the above picture, the front tires can see a bit more weight than the rear under hard braking.
the highest braking capabilities are much higher on the front than on the rear, therefore, we must ensure that those brakes are up to the task.
How do we do that?
Well, it all comes back to torque. Torque is just some force that acts over some distance. It is for this reason that you might use a longer bar on a wrench that you are trying to get a stuck bolt out with.
Let's say you are trying to stop a big heavy tractor tire from spinning. Imagine that you put a little brake pad from the front of a bike a few millimeters from the center of the wheel.  It wouldn't do much would it? Then imagine that you put that same brake, with the same pressure, as far from the center as you could.  Imagine that you could actually put it a few meters farther than the tire. In fact, let's go all the way and say that you could put that little brake pad a few skyscrapers away.  That same little brake pad could do a LOT more to stop that tire.  It would be no problem.
This same principle helps us exert the extra force that we now know front wheels can receive. So bigger diameter brakes up front help even-out the pressure required to stop the car. Those higher forces require additional thickness  to transfer those forces through the disk, and into the hub.