What's wrong with height?
A possible explanation for the gap between short people's success and that of tall people: Tall people may have greater self-esteem and social confidence than shorter people. In turn, others may view tall people as more leader-like and authoritative.
It sounds like there may be systemic heightism that pushes our society towards having a favorable view of tall people as compared to short, while either strengthening tall confidence and lower short confidence.
Sounds similar to the "studies" I hear about where they ask common people about white vs. black people and their perceptions.