I have to figure out, which of the two variables (BMI and Weight) is the dependent. So I can make a scatterplot. Can you please tell me which one? And why? I tried searching the internet, but without any luck.
It reads very like a study question, so I'll answer in the appropriate way (providing guidance not a direct answer) .
A dependent variable is one that depends on or can be derived from the others.
One of your variables is calculated from the other (in combination with additional information), so is the dependent one. I hope that is enough to work out which is which.
One of the reasons it's not widely compared is because BMI has been used in the place of weight. Different weights can mean different degrees of "fatness" for people in different heights. So, to make weight a bit easier to compared between people, BMI was used.
So, in a way, beware of very misleading analysis results: BMI is mathematically related to weight, and your model will appear as if it performs extremely well.
Yet, if you have other reason to do so, then my answer would be that there isn't any clean-cut causal relationship between them. High weight may result in high BMI but without knowing the height we don't know. Causally, we gather weight first, and then height, and compute BMI; but it does not necessarily mean we can't predict weight given an BMI and height, even it's less likely so.
Graphically, if your goal is to show how BMI can vary given the same height, then BMI at y axis, weight at x axis; if your goal is to show how weight can vary given the same BMI, then BMI at x axis, weight at y axis.
Often, when thinking about which is the DV and which is the IV, there's no clear statistical reason or even one derived from the experiment - if you manipulate one variable and not another then the one you manipulate is the IV. Here, you don't manipulate either.
So, you have to think about the two sentences "A depends on B" and "B depends on A" and decide which makes sense. If A was height and B was weight, it would be easy: "Weight depends on height" makes more sense than "height depends on weight" (even though, at least for adult humans, weight changes more easily than height does).
For your case, it's not really that clear, but I would say "BMI depends on weight" makes more sense than "weight depends on BMI".
Howver, whether a scatterplot of weight and BMI makes any sense (regardless of which goes on which axis) is another matter. I won't say such a plot can't make any sense in any situation, but I do wonder why you want to do such a thing and what purpose it is intended to serve.