Bertolt Brecht's performance of Die Moritat von Mackie Messer is sung with heavily trilled r's (see this YouTube video. I'd always put this down to Brecht having been born and raised in Augsburg deep in the South of Germany. (see this SE thread). But recently I've seen performances by other people who also use the trilled r's, so it seems to be the customary way the song is sung regardless of the singer's accent (see for example this YouTube of Ute Lemper's redition) Is there any significance to this? For example, since the singer is supposed to be a street singer in the opera, is there some strong tradition of street singing in Bavaria? Perhaps the accent is supposed to indicate that the singer is rural/urban, upper/lower class, educated/uneducated? Or maybe it's just meant to give the performance a grittier sound, or maybe it has no special significance and it's just a tradition. I'm just curious to know which is the case.
My answer consists of two parts:
1 - Deutsche Bühnensprache
In German the sounds
are free allophones. This means, that at any time each of these sounds can be replaced by any of the others without changing the meaning of any word. (Note that these sounds are not allophones in other languages!)
From this set the voiced uvular fricative ([ʁ]) is the most frequent realized version to pronounce the letter R by German native speakers, but the other two also appear quite often.
But the two trills have the advantage to be more different to all the other sounds, so using them adds more contrast to the speech and therefore makes it easier to be understood by the listener. And so the German philologist and professor for German language Theodor Siebs published a book about pronunciation of German on stages in 1898. This kind to pronounce German words is called Bühnendeutsch and still ist used in a modernized version by actors on all important stages where German is spoken.
Part of this Bühnendeutsch is the consequent usage of the voiced alveolar trill (the rolled R) when the letter R has to be pronounced. Today the pronunciation on stages is no longer as strict as 100 years ago, but when this kind of pronunciation was introduced, even words that end in -er like Wasser [ˈvasɐ] or bitter [ˈbɪtɐ] where no R has to be pronounced, but an [ɐ] (near-open central vowel), was pronounced on stages with an [r] at the end: [ˈvaser], [ˈbɪter], which in fact is a wrong pronunciation.
What you hear in this historic recording is the aim of a singer to pronounce the text as good as he can according to the rules of Siebs. But the result is a pronunciation that is far away form an average native speakers pronunciation. And this in fact is the main critique on Siebs's Bühnensprache.
It was even more criticized by native speakers living in southern areas of the German speaking region:
In the early years of 20th centuries the biggest city where German was spoken was Vienna (in 1916: 2,239,000 inhabitants) (Berlin in the same year: 1,771,491) (all over the world only New York, London and Paris were bigger than Vienna in those days) and the most important stage in the whole german speaking area was the Burgtheater in the very heart of Vienna, and it still is one of the most important German speaking stages. The standard pronunciation of German in Austria is different from the standard pronunciation in northern regions (Hamburg, Berlin, Köln). This has historic reasons, reaching back to medieval times. But Theodor Siebs, who invented German Bühnensprache, was born in Bremen, in the very north of Germany, and so his Bühnensprache reflected the northern way of German pronunciation, but Vienna is in the south, and so in Austria Siebs's Bühnensprache never was accepted by the audience.
The modern version of Bühnensprache still is close to the northern way of speaking German, but less strict as when it was invented. And something else has changed in the last 100 years: Today almost all German native speakers living in the south (Austria, Bavaria and neighboring regions) are bilingual without knowing it. They all speak German the southern way (influenced by Bavarian dialects) but also the northern version. This was not the fact 100 years ago, when Siebs's Bühnensprache was introduced. And also for this reason today Siebs's Bühnensprache is much more accepted in the south than it was when it was introduced.
2 - The murder ballade itself
A Moritat is called murder ballad in English. This type of ballades has a long tradition.
The story of Die Dreigroschenoper (The Threepenny Opera) is about a gangster called Meckie Messer (in the English version: Mack the knife) and in the song Die Moritat von Mackie Messer (The Ballad of Mack the Knife) the singer tells how cruel Mackie (Mack) is:
In the first verse he is compared with a shark (Mack's knife is like the teeth of a shark). Later it is said that when people fall down death, it was because Mack was there. A dead body at the beach? - Mack. But nothing can be proven. Mack is too clever.
So, the song is about a cruel and dangerous killer. In English there are many pirate songs that are used to be sung with a rolling R, and the reason is the same in both cases: The trill adds some thrill to the story.