Many west African languages also have a habitual be! With that grammatical function existing in both Irish and that group of languages, it's no wonder it stuck around in AAVE.
The interesting thing is, like someone else pointed out in the notes, that this habitual be continues to exist in Hiberno-English. However Irish people don’t say “I be climbing mountains on Mondays”. Instead they’d say “I do be climbing mountains on Mondays”. Teachers all over the country tell kids to stop their does be’s and do be’s.