On 2016 Feb 11, thomas samaras commented:

The paper provides excellent information on the body fat differences in different ethnic groups. Heymsfield et al. also provide convincing evidence that contemporary cohorts usually follow the height squared law [Quetelet Index (QI)] instead of the height cubed law [Ponderal Index (PI)]. However, there are significant exceptions such as data from the HES and HANEs findings (Advancedata Nov. 1976, p 8.). Based on about 6500 individuals, these findings show increasing weight follows or exceeds the PI.

Men 18-74 years: Actual weight: 172 lb vs. Predicted height cubed 
weight (PI): 171.2 lb

Women 18-74 years: Actual weight: 143 lb vs. PI: 140 lb

While there was a 10 year difference in the two populations, the QI did not apply. The increase in weight with height followed the PI (wt/ht3).

Another study (Heymsfield, et al. 2007) showed taller and shorter contemporary cohorts of men followed the PI as shown below:

Height 177cm vs. 174 cm: Actual weight of taller males = 80.6 kg vs.predicted height cubed weight
    (PI) = 80.8 kg 

Data from Cameron and Demerath (2002) showed the PI applied to contemporary 9-year old children as well. See below:

Heights: 135.8 cm vs. 132.1 cm: Actual weight of taller cohort = 32.4 kg vs.31.1 kg predicted by
    the PI.

Data from Heude et al. (2003) also found that 10-11 year old French children experienced a weight increase that was slightly higher than the PI between 1992 and 2000.

Over 80 populations worldwide follow or exceed the PI when different generations are compared. A few are reported in Medical Hypotheses 2002, vol 58 (Table 1): The actual weight for the taller group is compared to the predicted weight based on the assumption that weight increases as the cube of the increase in height or PI and not the square of height as in the Quetelet Index):

Harvard entrants (males)in 1930s vs. 1958-9: Actual wt: 73.7 kg vs. PI prediction: 71.5 kg                  

Wellesley entrants (females)in 1930s vs. 1958-59: Actual wt: 57.9 kg vs. PI prediction: 58.2 kg                         

Male school children in 1934-35 vs. 1958-59: Actual wt: 51.0 kg vs. PI prediction: 51.3 kg

Swedish males in 1971 vs. 1995 (n = 488,732): Actual wt: 72.1 kg vs. PI prediction: 68.0 kg                     

The reasons for taller people having the same or lower BMI/QI compared to contemporary shorter people may be that food portions are standardized so that taller people consume fewer calories per day and shorter people get relatively more. For example, independent of height, most people drink or eat one glass of milk, one hamburger, and the same size meal when dining out. Another factor is socioeconomic status (SES). Taller people are more often from higher SES compared to shorter people, and we know that in the West, poorer people tend to be more overweight or obese than higher SES people. The most likely explanation for this condition is that higher SES people follow healthier eating habits and are more attentive to weight gain. However, the BMI of taller people appears to be increasing. For example, Cohen and Sturm (2008) reported that shorter Americans had significantly higher BMIs than taller people in the past. However, in recent years, they found that taller people have been gaining in BMI at a faster rate than shorter individuals.

In conclusion, as the world population increases in height, weight increases at a rate that matches the Ponderal Index. That’s why the average US male in 1900 had a BMI of 21-23 compared to 26-28 today. Height since the 1900s has increased by 3 to 4 inches. Of course, much of weight increase is related to fat mass.

On 2016 Feb 11, thomas samaras commented:

The paper provides excellent information on the body fat differences in different ethnic groups. Heymsfield et al. also provide convincing evidence that contemporary cohorts usually follow the height squared law [Quetelet Index (QI)] instead of the height cubed law [Ponderal Index (PI)]. However, there are significant exceptions such as data from the HES and HANEs findings (Advancedata Nov. 1976, p 8.). Based on about 6500 individuals, these findings show increasing weight follows or exceeds the PI.

Men 18-74 years: Actual weight: 172 lb vs. Predicted height cubed 
weight (PI): 171.2 lb

Women 18-74 years: Actual weight: 143 lb vs. PI: 140 lb

While there was a 10 year difference in the two populations, the QI did not apply. The increase in weight with height followed the PI (wt/ht3).

Another study (Heymsfield, et al. 2007) showed taller and shorter contemporary cohorts of men followed the PI as shown below:

Height 177cm vs. 174 cm: Actual weight of taller males = 80.6 kg vs.predicted height cubed weight
    (PI) = 80.8 kg 

Data from Cameron and Demerath (2002) showed the PI applied to contemporary 9-year old children as well. See below:

Heights: 135.8 cm vs. 132.1 cm: Actual weight of taller cohort = 32.4 kg vs.31.1 kg predicted by
    the PI.

Data from Heude et al. (2003) also found that 10-11 year old French children experienced a weight increase that was slightly higher than the PI between 1992 and 2000.

Over 80 populations worldwide follow or exceed the PI when different generations are compared. A few are reported in Medical Hypotheses 2002, vol 58 (Table 1): The actual weight for the taller group is compared to the predicted weight based on the assumption that weight increases as the cube of the increase in height or PI and not the square of height as in the Quetelet Index):

Harvard entrants (males)in 1930s vs. 1958-9: Actual wt: 73.7 kg vs. PI prediction: 71.5 kg                  

Wellesley entrants (females)in 1930s vs. 1958-59: Actual wt: 57.9 kg vs. PI prediction: 58.2 kg                         

Male school children in 1934-35 vs. 1958-59: Actual wt: 51.0 kg vs. PI prediction: 51.3 kg

Swedish males in 1971 vs. 1995 (n = 488,732): Actual wt: 72.1 kg vs. PI prediction: 68.0 kg                     

The reasons for taller people having the same or lower BMI/QI compared to contemporary shorter people may be that food portions are standardized so that taller people consume fewer calories per day and shorter people get relatively more. For example, independent of height, most people drink or eat one glass of milk, one hamburger, and the same size meal when dining out. Another factor is socioeconomic status (SES). Taller people are more often from higher SES compared to shorter people, and we know that in the West, poorer people tend to be more overweight or obese than higher SES people. The most likely explanation for this condition is that higher SES people follow healthier eating habits and are more attentive to weight gain. However, the BMI of taller people appears to be increasing. For example, Cohen and Sturm (2008) reported that shorter Americans had significantly higher BMIs than taller people in the past. However, in recent years, they found that taller people have been gaining in BMI at a faster rate than shorter individuals.

In conclusion, as the world population increases in height, weight increases at a rate that matches the Ponderal Index. That’s why the average US male in 1900 had a BMI of 21-23 compared to 26-28 today. Height since the 1900s has increased by 3 to 4 inches. Of course, much of weight increase is related to fat mass.