The limiting factor is the bend. The subatomic particles want to go in a straight line. A magnetic field is used to bend the beam around into a circle. The faster the particles are moving however, the more energy is needed to bend them. A larger circle has less bend. This lets you get your particles faster.

Since E^2 = M^2 C^4 + P^2 C^2 (the full form is E=MC^2 ). If you can force the particle to stop rapidly, then you can force the energy from momentum into mass. This is done by hitting 2 beams into each other. The faster the beams, the more energy is available to convert to mass.

Most of the time, this creates a lot of mundane particles. However, ever so often it creates something interesting. They rapidly decay into mundane particles, but the shower they create tells us a lot about them. The catch is that all the energy needs to be present at once. You can't use more particles, you need to make them move faster.

As for why. The more particles we have to study, the more we can figure out about the underlying rules. We have a number of theories. They all agree at lower energy levels, but disagree at higher energy levels. By knowing which is correct, we can pry deeper into the workings of reality.

More size = more speed and more particles colliding = more bang = more data = for example possibility for dark matter and/or heavier particles to be found.