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Let's do the math (based on [1]):

If I weigh 85 kg and measure 185 cm (BMI 24.8, right at the edge between normal and overweight), my body surface to wash is 2.09 m². Let's assume a 3-minute shower at 15 liters per minute, so 45 liters of water. So 21.53 liters per m².

If my weight is 120 kg (140% of above) and I still measure 185 cm (between Obesity I and II), then my body surface to wash is 2.42 m², an increase of 0.33 m². Applying the same ratio as above, at 21.53 liters per m², I would need 52.11 liters of water (115% of above).

So a weigh of 140% results in a water consumption of 115%.

Qualitative argument is right, but the effect is not linear.

[1] https://stats.areppim.com/glossaire/body_mass_def.htm

That assumes time to wash is linear to surface area. It is harder for heavy people though to wash themselves tho, harder to reach everything including tools, more tools required, more time spent not actively washing while the water runs.

OTOH, the more sizable the body the less water it takes to fill the bathtub.

I need more time to shower when I exercise, probably could save a lot of water by shaving my head.