That is a stupid way to measure how much one should pay in tax, honestly.
You rent, electricity, food and clothing doesn't go up because you double your income (unless you move, but then you presumably get better housing too). Why should your tax?
I'll assume you're trolling but the relatively inelastic nature of fix costs like room and board, food, entertainment etc. is part of the reasons for promoting a progressive tax system. Those who have made fortunes here in the us are likely those who have benefited from federal and state oversight and infrastructure, which is an additional justification behind taxing the wealthier members of society at a progressive rate.
For the anecdotal insight on this: paying about 20k a year in federal taxes with my current annual salary is nothing compared to the impact of the 5k or so a year in taxes I paid when I was a poor waiter/college student in terms of its impact on my budget. At this point I could easily pay out an extra 10 or 20k with out severely impacting my quality of life or rate of savings; corollary, a few extra thousand back when I wasn't making all that much money would have been the difference between sleeping on an air mattress versus a real bed, or having enough good (as in nutritionally worth while) food to eat.
Most people do move to better housing, buy more expensive food/clothes and use more electricity when they double their income. And as that doubled income doubles, the amount they are willing to pay for/use those items also goes up. Just as the amount they are willing to haggle for these items goes down (note: I'm talking about majority, I know there are exceptions).
You rent, electricity, food and clothing doesn't go up because you double your income (unless you move, but then you presumably get better housing too). Why should your tax?