a meta-analysis of weak studies is a weak meta-analysis

Meta-analysis sits high on most evidence hierarchies and gets treated as authoritative regardless of what went into it.

What it does well: increases precision when combining comparable, unbiased studies of the same question.

What it can't do: remove bias present in every input (if all the studies share a flaw the pooled estimate has it too, with a tighter interval, precision without accuracy). Fix publication bias (pooling a selected literature preserves the selection). Combine incomparable things (different models, doses, routes and endpoints pooled into one number describes nothing in particular).

So the question is always what went in. A meta-analysis of twelve small unblinded animal studies is twelve small unblinded animal studies with a summary statistic attached. Methodological point, applies to any meta-analysis you run into.