The original Leibniz’s question „Why is there something rather than nothing?” is rephrased in a „weak” way: „Why is there a lot of things rather than almost nothing?”. The first part of the article argues for two propositions: 1) We may not reasonably expect a real answer to the original Leibniz’s question, mostly because the concept of „nothingness” cannot be defined in a way that makes sense and is operational. 2) The „weak” version of the question retains the philosophical „spirit” of the original. In the second part a methodology for answering the weak Leibniz’s question is presented - one of an analysis of the cosmic evolution in terms of the reasons and causes for the emergence of new types of natural objects and processes („things”)...