The question is framed on a very simplified concept that leaving aside actual prices of products and services, there is little difference in actual quantity of resources consumed by any particular individuals on a daily basis.  A rich person can afford to buy expensive products and services, while a poor person must be satisfied with less expensive things, but the same amount of infrastructure is required to transport a pound of product, travel a given distance, etc.  Based on that information, then why should the rich pay more total dollars in taxes than the poor for using the same infrastructure?

The question is missing a key fact though.  Consumption is only one factor involved in taxation.  (Actually for consumption the question is already partially answered with sales and use taxes.  It doesn't matter whether rich or poor, everyone pays sales and use taxes only on products and services purchased.)

Another important factor to consider is how much infrastructure is required to produce each dollar of income. When that fact is taken into consideration then someone making a million dollars a year is utilizing much more of the infrastructure than someone making ten thousand dollars a year.  For this reason income taxes and capital gains taxes are calculated based on earnings and profits.

To answer the original question about fairness though, an even more important consideration is actual benefit received from the system.  Much is made lately about government entitlements to the working class, but I don't imagine any millionaires out there would be willing to trade places with someone that needs their income supplemented to meet basic needs.  The wealthy are already receiving much more benefit from our economic system than anyone receiving any benefits from government assistance.

For this reason it definitely is fair that a billionaire should pay more total dollars in taxes than a millionaire, a millionaire should pay a larger total than a $200,000/yr earner, and they should all absolutely be paying more than an average working class person.  The wealthiest people in our society receive the most benefit from the economic system we have and should reasonably be expected to pay more taxes to support the infrastructure required to maintain and even improve that system and society.