What's the grammar behind "[Noun/pronoun] + [be] + [gerund]"

I'm wondering what's the grammar behind phrases like:

• We be eating


• She be sleeping


• etc

What are the grammar backgrounds for phrases in such form? Can there be any other use cases of such grammar constructions?

Answer

This is a feature mostly (but not exclusively!) of English as spoken by Black Americans, called African American Vernacular English (AAVE). This use of be is called the invariant be or habitual be.

To use your example, with the corresponding "standard" English meaning,

• "We be eating" = We eat (as a regular or recurring event or state)


• "We be sleeping" = We sleep (as a regular or recurring event or state)

Do not use this construction in "standard" English, or anywhere you may be misunderstood, because
a) it's incorrect in "standard" English
b) it may be taken as mocking how someone else speaks.