Solution 1:

Marcus_33's answer led me to some interesting reads. Hip Hop in America: A Regional Guide provides further details:

Mainstream America was first introduced to the St. Louis accent and slang—a mix of rural Southern and Midwestern terms and pronunciation—via Nelly. . . . "Hot in Herre" did not only send Nelly to the top of the charts, but it emphasized the way natives of this area pronounce words differently. Most notable is the pronunciation of the "e" sound in many words. Instead of saying "here" they say "hur." The words "thurr" (there), "wurr" (were), and "urr'body" (everybody) are also recognizable in lyrics from St. Louis.
. . . .
As a whole, the dialect situation in Missouri is diverse. The accent featured in the hip hop culture is exclusive to the large African American population. This speech creates a "country" sound by mixing "Southern drawl and Midwest twang." The rest of St. Louis has a distinctively different speech.

A post called "Right Thurr" on Dialect Blog adds:

Raymond Hickey, a linguist who studies Hiberno-English, notes a similar shift in middle-class Dublin accents in which the vowel in ‘square’ is pronounced (as in AAVE) with a vowel similar to American ‘nurse.’
. . . .
My only guess for how this might relate to African-American English is that it’s one of America’s non-rhotic (r-less) dialects. Is it possible that, for African-Americans attempting to speak rhotic English, they somehow make the same hypercorrective ‘mistake’ that Hickey’s Dubliners do?

Solution 2:

Shortening every to err appears to have been popularized with the St. Louis rap scene in the mid 2000's.

St. Louis rap group Da Hol' 9 released a song in 2003(re-released in 2009) titled "Urbody in the Club Up"

The first major charting single containing the pronunciation is the 2004 hit "Tipsy" by J-Kwon (also from St. Louis), where everybody is pronounced errbody.

In 2005, Nelly - perhaps the most famous St. Louis-born rapper - released a track titled "Errtime".

Prior to these songs (particularly "Tipsy"), references to the spelling are very scarce on Google - blog posts and YouTube comments show up, but with no regularity or connection. After "Tipsy", the spelling seems to have expanded quite a bit.

Solution 3:

Though 'AAVE' (African American Vernacular English) is a good general bet.

The recent popular use of this pronunciation (in media) may stem from a Bill Cosby performance, where he stresses that pronunciation heavily. Bill Cosby is a much-appreciated US phenomenon, by all races.

It has since become a meme.

Solution 4:

Every Christmas back in the 60s, a Scottish aunt used to send me that year's Oor Wullie annual.

As the Wikipedia link says, it's a comic strip that appears (or at least, used to appear) every week in The Sunday Post. I don't think I've ever seen a copy of the paper itself, so I've never seen the strip in its "natural habitat". But the front cover of each annual album always had the tagline...

Oor Wullie! Your Wullie! A'body's Wullie!

...where obviously A'body is intended to be the casual Scottish pronunciation of Everybody.

So black American rappers a couple of generations later aren't saying anything new there.