We take a preponderance of correlation as evidence, but we can't really provide rigorous proof. I mean, imagine what a double blind study to, say, 'prove' that smoking causes lung cancer would entail. The ethics of causing something we have reason to suspect is harmful to a population sample is ethically extremely problematic; hence, all we frequently have is correlative.
Even when it's something there isn't as big an ethical issue for it's usually not single blinded, let alone double. Diet, for instance; the groups know what they're eating. Did the differences happen because of the different diet, or because of something else (such as increased energy leading to more exercise, or the perception that they were eating 'healthy' lead to them actually becoming so, or picking up other healthy habits? Etc).
As I said, establishing causation -with any degree of rigor-, is basically impossible. Otherwise we're just left with "hey, a whole buncha correlative studies indicate this, so, maybe take it as true?"