Heidegger likes this question a lot.
A good book on the subject is T. A. Tymieniecka with the question as the title.
I see that there are now several books with this title and on this subject. What I want to mention, is the same thing I have mentioned with respect to other questions which is that Being is unique to the Indo-european languages. So when we say “why IS there something rather than nothing” citing Being rather than Existence has a subtle effect.
Hegel was quite clear in his Logic that when he said “nothing” as the opposite of Being that he meant Buddhist emptiness. He said that the synthesis of Being with Emptiness is Heraclitian flux out of which comes the determinate thing which is called Dasein.
Heidegger on the other hand plays word games and says that nothing means NO THING which to him means that it Being is not a specific thing, which is really another way to talk about what he calls ontological difference, i.e. the difference between Being and beings. Specific beings are called ontic, so Ontological Difference is between Ontology/ontic.
Hegelian nothing is Buddhist emptiness which is nondual. Heideggarian nothing is merely the negation of the ontic entity with Being.
Interestingly Dasein, even though it has “Sein” in it is used to indicate existence in German philosophy. Heidegger uses this term for the human existent in Being and Time. He uses the fact that existence also is related ecstasy and considers the upwelling of Being in dasein as that ecstasy.
However, this kind of existence that is Dasein for Heidegger never frees itself from Being and so the fact that “sein” is There (i.e. there being) is appropriate in the case of Heidegger.
Hegel because he relates nothing to emptiness of Buddhism is actually referring to existence in one of its nondual interpretations.
In the Western tradition existence is always seen as a primordial dragon that is there to be slayed (Python, Typhoon) as in St. George and the dragon primal scene.
In our tradition existence comes in later from the Arabs that preserved the Greek tradition. In arabic existence is called wajud which means what is found. The used kun (make) as a technical term for the surplus of Being over existence. So when the Greek tradition came back into latin the word existence was made up to cover this difference that was not there in the Greek tradition itself prior to its assimilation by the Arabs.
So Hegel actually is deeper than Heidegger in this respect because when he says nothing he really means of the nondual interpretation of existence that is propounded in Buddhism as an antidote to SAT (Being) in the Hindu/sanscrit Indo-european tradition.
Hegel realizes that existence as nondual is there beyond the projections of Being, where as for Heidegger existence really only means the dynamic upwelling of Being itself in dasein as the world is projected.
So the question why is there something rather than nothing? would mean completely different things to Hegel and Heidegger. For Hegel it is the relation between determinate being and nothing mediated by Being. For Heidegger it is the the relation of ontological difference between “some thing” and “no thing” where Being itself is No thing. In ontological difference Being withdraws, so the IS in the statement withdraws and is only seen as no thing in relation to something.
This shows that there are different nuances in interpretation of the words in the statement, so that there can be very different interpretations of what appears to be a very straight forward question.