BE syntax

[Wilson Gray]

One night, while listening to The Blues Express, a program carried by
XPRS, a powerful, semi-legal radio station with its offices in Del Rio,
TX, but with its transmitter located in Mexico, I heard the DJ say:

"I'm just sitting here, eating me some potato chips."

The very next night, I heard the same DJ say:

"I'm just sitting here, eating on me a hamburger."

FWIW, my intuition is that he made this distinction because potato
chips come as relatively small, individual pieces that can be eaten in
one bite, whereas a hamburger can be eaten only piecemeal, hence
requiring several bites.

-Wilson Gray