A church's hierarchy today--and I am focusing on Protestant rather than Catholic church hierarchy--reflects the wealth and social standing, either overtly or covertly, of the membership. No matter the denomination--Presbyterian, Methodist, Baptist, Lutheran, Christian Evangelical (and many others)--the wealth and social standing of members place those members near the top of any church's hierarchy. This model goes back to the earliest churches in the American colonies, particularly the Puritan Church in New England in the 17thC. through the mid-19thC.
One can argue that, at least with respect to the Puritan Church, which had a firm hold on the colonies in New England, the wealth and social standing of church members were very important in placing church members within the church hierarchy. And we can argue further that, despite the Christian doctrine that "Blessed are the meek, for they shall inherit the earth" (Mark 5:5), the most important church in New England placed the wealthiest church members near the top of the church's hierarchy:
An important social role of the deacon was to be part of the seating committee that mapped out the social hierarchy of the congregation: church membership, age, gender, race, wealth, public office, education, and reputation all were calculated to determine where each congregant would sit. The closer the person sat to the minister, the higher his social (and presumably spiritual) status. (http://cdm.reed.edu/cdm4/indianconverts/studyguides/social_hierarchies/church_hierarchies.php)
Wealth and social standing, as well as church membership, then, became primary indicators of a church member's rightful place in a church congregation, and if we were to look at the seating chart of a typical Puritan church (from the early 17thC. into the mid-19thC.), those members who were wealthy were seated closer to the pulpit than poorer members. A church member's wealth and social standing became an indicator of that member's value in God's eyes and, more important from a practical standpoint, in the eyes of the church leadership.
It is misleading, however, to suggest that the Puritan Church and later Protestant churches in colonial America and the early years of the United States believed wealth for its own sake made a member more valuable than another. Puritans and other Protestant denominations firmly believed that
“Riches may enable us to relieve our needy brethren, and to promote good works for church and state.” Money exists “for the glory of God and the good of others.” “The more diligently we pursue our several callings, the more we are capacitated to extend our charity to such as are in poverty and distress.” (http://www.apuritansmind.com/stewardship/rykenlelandpuritansandmoney/
Even though one's standing within the church hierarchy might be influenced by one's wealth, a wealthy person was presumed to use his or her money to make better lives for the less fortunate. Private, rather than institutional charity, was a hallmark of the American church, no matter the denomination, and wealthy members were valued because, at least in theory, their money could help alleviate the poverty of other church members.
Although no Christian church would openly state that wealth marks a member's importance, in the 20th and 21st centuries, as church membership continues to decline--from 1958-2008, Protestant churches lost 25% of their members--it is reasonable to assume that the wealth of remaining church members will keep those members at the top of church hierarchies. As churches throughout the country struggle to survive, let alone grow, their survival depends largely on the wealth of their congregations and the willingness of their congregants to support that survival. By default, the wealthiest congregants of any church will be, again, either overtly or covertly, at the top of the hierarchy.
I can't say that I see a direct or inverse correlation between wealth of a congregational member and their heirarchy within the church. That doesn't mean there isn't one at certain churches or denominations but I can't say that I have come across evidence of it. Anecdotally, I have been asked to be an elder at my church. I'm 33 and make less than $50000 per year. I know there is an elder now that is twice my age and makes well over 4x what I make. If I see any kind of hierarchy, I would say that it is more along the lines of how long someone has been a member of the church. That then would be a direct proportion. Longer membership, then a higher level on the hierarchy.