Here’s another study on IQ & weight/height ratio but this time the data is from 2007 instead of 1974 and the sample size is 6,798 people (in the UK) instead of just a few hundred Americans. In this study, for those with IQs around +1.66 SD, obesity puts you at the +1.07 SD of the normalized BMI distribution of your IQ group, but for those with IQs around -1.66 SD, obesity puts you around +0.8 SD. In other words, a 3.33 SD change in IQ (50 points) is associated with a 0.27 SD change in weight/height ratio. This suggests a standardized regression slope (and thus correlation) of 0.27/3.33 = -0.08.
It makes sense that the negative correlation is low given that there are so many incredibly overweight people who don’t seem the slightest bit stupid.
It would be nice to see a study that got beyond simple BMI and compared IQ with fat-free mass index and muscle-free mass index so we could see what type of weight is driving the negative correlation or if they both contribute equally. One theoretical possibility is that people with bad genes have both low IQ and high BMI, but with hard work in the gym and a little help from steroids, you can turn that high BMI into rock solid muscle.