The simplest example I can come up with is the weight - the density of humans is probably constant for practical purposes and therefore the weight must be positively correlated with your body dimensions. It is also pretty obvious that humans, or tissue for the matter, does not grow in a strongly directional manner. If you gain weight more or less all dimensions not constraint by your skeleton will increase, i.e. you will probably not end up with a wide but flat or narrow but thick belly.
I wouldn't say density is a constant. Muscle weighs more than fat for the same volume, as does bone. Same height, higher muscle or denser bone structure, and you can have wildly different weights. Makes simplistic measurements like BMI pretty laughable - look at pretty much any athlete, who would run high over-weight or obese according to BMI.
That doesn't matter, humans are a lot of water and the density of humans seems - after a quick search - to be essentially within the density of water plus or minus ten percent. In this context that's constant enough for me and definitely way to small to possibly offset the variability in body weight.
That is way I said not constraint by your skeleton - or what ever else. The point is that at least some dimensions are obviously correlated, not that all dimensions have to be correlated.
>weight gain in adulthood doesn't cause you to get taller //
Not even a tiny bit, like because of fat feet or more fat on the head? Not trying to be facetious, just seems huge people have fat feet and that there's likely to be a little fat on the bottom of the foot. Mind you that's going to be countered by compression of the spine, so there could be a inverse correlation?