The press release accurately reflects the main findings of the study. It is a study of very good methodological quality, with results that support the conclusions reached. However, it should be borne in mind that this is a Mendelian randomisation study and, therefore, the exposure variables of interest in this work, body mass index (BMI) both in childhood and in adulthood, are not measured directly, but through the so-called instrumental variables, which in this case would be genetic variables strongly related to both BMIs.

There is much scientific literature that supports the relationship between BMI and psychiatric disorders, although the main novelty of this study is the fact of studying BMI in childhood.
The translation of the results of this study into practice presents a duality that must be taken into account. On the one hand, the fact that a higher BMI in childhood is related to a higher risk of schizophrenia in adulthood adds to the already strong scientific evidence for the benefits of BMI control in childhood. However, the fact that a higher BMI in adulthood is associated with a lower risk of schizophrenia and obsessive-compulsive disorder would not have a clinical application, as such an increase in BMI would imply a higher risk of cardiovascular diseases, among other pathologies.

A lot of caution in the face of an article which, on the other hand, says nothing that our ancients did not already know: mens sana in corpore sano.

The press release starts off well but then sells the method (Mendelian Randomization) as if it were equivalent to experimental randomization, which is everyone's wish, yet to be proven.

Regarding the article, as a statistician I should thoroughly review their methods, check that their programs work and actually do what they say they do. Ideally, I would have to access their data and see that I can reproduce their methods, which would obviously take more time than any reader has. Therefore, given the boldness of its title, I will explain why this study should be considered as a simple idea that is released to the community, not a scientifically proven result, which requires that others can reproduce the methods and replicate the results in new data. For the sake of brevity, I will focus on two aspects.

The title talks about effects, which is reserved for experimental articles that randomise an intervention and wait in time to collect all its possible effects, the desired positive ones, but also the unexpected ones. Inside they clarify that they are looking for causes, which is always tentative as it requires the statistical model to be complete (Draper). That is, it correctly includes all predictor variables (possible confounders) but no more, which could lead to selection bias (Hernan). Thus, the assumptions about causes are so bold that they require new studies on effects which, I insist, must randomly assign an intervention. That is, an action that can depend on the will of the researcher, always with the consent of the volunteer.

They abuse the p-value, a popular statistical tool, albeit a very fragile one since, among other things (ASA statement) it facilitates the horrible practice known as data dredging or p-hacking. But I do not have access to supplementary table 1 where the authors should detail in which section of their manuscript they report the 20 crucial items required by the STROBE-MR guideline that apply to ‘Mendelian randomisations based on observational data’. Your item 3 asks to specify which hypotheses were prior and which were not, which I have not been able to find in the text. If they are posterior, the results should be considered as suggestions rather than proven scientific results.

In short, a lot of caution with this article, which requires a very deep critical study.