Conjecture

The size of each dimension is most likely a result of how much momentum is travelling in the corresponding direction. The impact of this is immense, which is still an understatement. The speed of light c, if similarly controlled by dimensional size, is the ratio of the time and spatial dimension. All the forces and particle masses and coupling strengths are a result of which the amount of momentum travels in which direction. The only fundamental constant that is left to explain is h. I believe there are stability reasons that make the values we have, the most probable values, but they could have been different by 1%. The butterfly effect, chaos theory, means the universe wouldn't be different by only 1%. Things would be much different.

The interesting thing to explain is why some dimensions are exactly the same size. If one normal macro space dimension were 10% longer than another one, this asymmetry would be very noticeable. Gravity would be 10% weaker along that dimension. I expect that, just as each degree of freedom in a system gets an equal amount of energy, that when two sizes are close that they tend to equally divide.

The question then becomes why aren't all dimensions this large. Once some momentum gets into a stable state it holds the momentum in that dimension, preventing its interaction that could equalize the momentum. The ultimate answer lies in the topology of many dimension spaces. See Srinivasa Ramanujan.