Why do we say "Half a loaf is better than none"?

Meaning:

It's better to have something, than nothing at all.

Background:

This expression is first recorded in John Heywood's 1546 book of proverbs:
Throwe no gyft agayne at the giuers head, For better is halfe a lofe then no bread.

John Heywood (c. 1497 – c. 1580) was a 16th century English dramatist employed as a singer, musician and playwright at the court of Henry VIII, and, later, at the court of Henry's daughter, Queen Mary. When the Protestant Elizabeth I succeeded to the throne in 1564, Heywood (a Roman Catholic) fled to Belgium where he stayed for the rest of his life. He is considered important to the development of English comedy, and is also remembered for his epigrams, proverbs and ballads.

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