I think it was just done that way to squeeze more bombs in the bay. The He-111 was initially developed as a civilian transport to circumvent the restrictions of the Versailles treaty, it even had a different, airliner-style cockpit.
I guess it wouldn't take much for an allied engineer/designer or an intelligence analyst to take a look at a few photos and identify its potential for bombing if it had been built with a cavernous fuselage from the start.
My assumption is that they went with a narrower fuselage partly to maintain appearances and partly because it was indeed used in civilian roles as well (mail carrier, etc), but when it was converted to a bomber this limited available bomb loads, hence the vertical bomb storage.
If you compare it with the Ju88 for example (which was designed and built as a pure bomber), you'll see that the 88 not only used a horizontal bomb bay arrangement but it also had dual bomb bays.
That being said i'm not 100% certain of this, i'm just piecing together known bits of information and making a reasonable assumption. I could still be wrong and they might have had a different reason altogether
