I don't know that I consider this a bullying issue, but perhaps an example of "food insecurity".

Has this child had anyone check into his home situation? He may not readily have access to regular on-time food and so when presented with an "opportunity", he acts as he sees appropriate.

My husband had limited food as a child. As a result, he became somewhat of a "hoarder" of whatever excess was available. To this day, he will sit at a table and "protectively" cover his plate with his hand as he's eating. He's nearly 50.

PLEASE check that this so-called bully is receiving proper nutrition.