Check out this chess programming wiki article [1] for a (still fairly hand-wavy) rationale for similar piece values, and the Wikipedia article on chess piece relative values [2] for a more in-depth look at various weightings. Some modern approaches use analysis of a huge corpus of master games to come up with piece values, but many of the systems are based on intuition and empirical evidence.
[1] https://chessprogramming.wikispaces.com/Simplified+evaluatio... [2] https://en.wikipedia.org/wiki/Chess_piece_relative_value