In my world, I have relatively robust humanoids as the focal human sub-species, and a number of other human subspecies that are more gracile in build. I wanted to work out roughly how much they would realistically weigh given their builds and heights.
In my research, I've used prehistoric humans as baselines. Neanderthals were shorter, but more robust than equivalent Sapiens. Homo floresiensis added in as an additional data point. These are the figures:
- Neanderthal average: 164cm tall (5'5"), 77kg
- Upper paleolithic Sapiens avg.: 179cm tall (5'9"), 67kg
- Late upper paleolithic Sapiens avg.: 166cm tall (5'4"), 62kg
- Floresiensis est.: 109cm tall (3'7"), 25kg
This works out to Neanderthals having 0.49kg/cm, Sapiens having 0.37kg/cm for both, and H. Floresiensis 0.23kg/cm. However, square-cube law being what it is, scaling these up to make, say, a 6-foot Neanderthal gives a weight of 89kg which is not too far from the expected weight for a real-life gracile Sapiens according to BMI calculators. Not very realistic.
Perhaps it's just been too long since I took a maths class, but I can't work out what sort of formula to use to be able to plug height and a 'robustness ratio' into to be able to get a realistic weight for scaling humanoids up and down.
Criteria for a strong answer
Ideally, any calculation would be viable for calculating a realistic weight for anything from goblins up to giants. Another option for a successful answer would be a BMI chart that is scaled far enough to encompass goblins or giants.
A stellar answer would propose a method of calculation, and provide an example of it in practice that matches the figures for prehistoric humanoids above.
Edit: Played around a bit with the NHS BMI calculator.
Seems to be that Neanderthals had an average BMI of 28.6, Sapiens 20.9/22.4 respectively, and Floresiensis 21. Playing around with the calculator gave me a 6' Neanderthal as weighing 95kg with the same BMI, whereas a 6' late upper paleolithic human would weigh 75kg.
I believe this is relatively realistic for humanoids that do not differ too greatly in size to require physiological adaptations to large weight. However, it doesn't let you plug number in for 3m tall people so doesn't quite cut it. Could be useful for checking answers though.