I found one sentence:
Jockeys must be of diminutive size for their horses to compete.
Why is there "of"?
Is it wrong to say "must be diminutive size"?
Could you explain the usage of this "of"?
"Diminutive size" is a noun phrase.
While noun phrases can be the complement of "be", they always indicate the identity or nature of the subject, not a property associated with it: a person can be a teacher, a human, a child, a monster, a tyrant, your uncle, the King of France, or (figuratively) a dinosaur; but a person cannot be a size, diminutive or otherwise: sizes are fundamentally different kinds of things from people, in fact from any kind of physical object.
Adjectival and prepositional phrases, on the other hand, can express a property or quality of the subject as opposed to its identity. So the jockey can be diminutive, or of diminutive size, but he cannot be (the sme thing as the abstract concept) diminutive size.
I, Ribo Flavin, being of sound mind, do hereby bequeath to my nephew, Uber Flavin, the sum of $40,000 (forty thousand dollars) for being so helpful to me in my declining years.
"Of sound mind" is not really different from any other prepositional phrase (e.g., up the tree, down in the dumps, to the store, at the wall, between the cars, etc.), including your "of diminutive size." Although unnecessarily wordy it is acceptable.
I, however, like you--save for my omission of one word--prefer the simpler and less wordy
Jockeys must be diminutive for their horses to compete.
be of is a phrasal verb meaning: English - OLD
1. possess intrinsically; give rise to. "this work is of great interest and value"
So you can be of sound mind, be of good cheer--but you can't be good cheer.