Just an example: The poorest 5 percent of households use 247 gallons of gas per year, on average. The richest 22 percent, with incomes over ten times higher, each use about four times as much.
The basic issue is as wealth increases people spend more on services which have lower energy needs than say food. A cheeseburger takes not just energy to cook much energy to manufacture. An account on the other hand uses much less energy per dollar spent.
https://www.epa.gov/energy/electricity-customers#commercial