How does the amount of water usage affect amount of energy usage?

Water has to be treated before you use it. That takes energy.

Then it has to be delivered to you. That takes energy.

Once it's delivered to you, you might heat it before you use it. That takes energy.

After you use it, it has to be treated again as sewage. That also takes energy.

How much? Here's a rough estimate I found for the UK:

"Water delivery and sewage treatment costs 0.4 kWh/d per person. The total energy use of the water industry in 2005-6 was 7703 GWh. Supplying 1 m3 of water has an energy cost of 0.59 kWh. Treating 1 m3 of sewage has an energy cost of 0.63 kWh. For anyone interested in greenhouse-gas emissions, water supply has a footprint of 289 g CO2 per m3 of water delivered, and wastewater treatment, 406 g CO2 per m3 of wastewater. Domestic water consumption is 151 litres per day per person. Total water consumption is 221 l/d per person. Leakage amounts to 57 litres per day per person."

See related link for more information.