Meta-analysis can never follow the rules of hard science, for example being double-blind, controlled, or proposing a way to falsify the theory in question. It is only a statistical examination of scientific studies, not an actual scientific study, itself.
A weakness of the method is that sources of bias are not controlled by the method. A good meta-analysis of badly designed studies will still result in bad statistics. Robert Slavin has argued that only methodologically sound studies should be included in a meta-analysis, a practice he calls 'best evidence meta-analysis'. Other meta-analysts would include weaker studies, and add a study-level predictor variable that reflects the methodological quality of the studies to examine the effect of study quality on the effect size.