Spanish document from Rota in 1873
Many people have heard of the Kabesa branch of the Flores clan. So many Chamorro leaders in government, education and religion come from the Kabesa family.
The Spanish word cabeza means "head." It can mean the literal head of a person, or symbolically the head of a household or the head of a business or what have you.
In the Marianas during Spanish times, villages were divided into neighborhoods called barangay. The head of each barangay was called the cabeza de barangay.
In the Spanish document from Luta (Rota) seen above, you can see that two cabezas de barangay, Francisco Mangloña, and Benigno Mangloña, signed the document. Francisco abbreviated his name in the usual manner; Fran.co.
It is possible that someone from the Kabesa family was so-called because he was a cabeza de barangay.
I also heard another version that the first man nicknamed Kabesa had a big head. But I am less inclined to believe that story.