What do you mean by "etymology"? That term refers to the origin (usually of the meaning) of a word.
Do you mean the historical origin of where that allophone comes from in the history of American dialects?
It's very difficult to trace the exact origin of sound features in dialects given that we only have recordings from the last 100 years or so, and because it isn't a simple answer in most cases.
The basic process is lenition (that is, weakening*), where the full stop is reduced to a much shorter gesture in the same location. I imagine this occurs naturally in many languages and dialects, just very rarely and not systematically. For some speakers of American English it occurred rarely and naturally and then started to become more frequent, and eventually, due to sociolinguistic reasons, the way those speakers spoke became the norm.
(*Technically in this case we could also consider one of the motivations to be assimilation to the non-obstructed articulation of vowels, where a tight/long stop closure was weakened to being a looser/shorter closure more like the open articulation of the vowels that surround it. Stop lenition occurs often, as in Spanish for example, where stops become fricatives between vowels.)
