The number 8 character in most fonts has a slightly larger bottom circle than top circle. Why is it designed that way?
Fonts are a variation on a theme. There are simply more possibilities for exploration if you let go of perfect symmetry. When you start exploring you will find that being asymmetric has some benefits. To take an arbitrary example, say that you're designing a readable font and you expect the print when worn out so that the middle is not visible. Then being asymmetric can help.
But mostly I would say that the shape is asymmetric for a similar reason B or say the & symbol's loops have a different size. A human hand has a hard time doing them exactly the same. Fonts have are heavily influenced by how handwriting has evolved.
Unless the typeface is designed to be geometric most typefaces will not have a numeral 8 that is symmetrical top-to-bottom. This is because the numeral would then appear to be extremely top-heavy.
There are actually a lot of fonts that have a symmetrical numeral 8. They are usually found under Geometric Sans or Modular fonts.
Some examples include:
ICT Serif Gothic