Question: The basic meaning of overhead is "above one's head"

However, in business field, usually An overhead cost or expense.
‘overheads, such as lighting, equipment, and any little extras, are paid for out of a centralized fund’
[Overhead (business) - Wikipedia](https://en.wikipedia.org/wiki/Overhead_(business))[Overhead (business) - Wikipedia](https://en.wikipedia.org/wiki/Overhead_(business))

In computing field,
In computer science, overhead is any combination of excess or indirect computation time, memory, bandwidth, or other resources that are required to perform a specific task.[Overhead (computing) - Wikipedia](https://en.wikipedia.org/wiki/Overhead_(computing))

So the key extending meaning is 'indirect and excess'.

I really unable to relate the meaning to "above one's head"?
What can I discern might be 'dangerous', 'pressing', 'important' above one's head?

Is there a fable or a proverb about this?

Answer: 
The key is not, as you say, "indirect and excess" but "unavoidable costs incurred when performing work". It is the same for brick-and-mortar business establishments and for digital computation. The "work" may be different but the *core* concept of **overhead** is the same. 

A business needs lights; a program needs electrical power; a business needs records, a program needs persistent memory, and so on.

As a mnemonic, the overhead of a brick-and-mortar business is "the roof overhead" (think part for whole, so the building and everything that goes with the physical establishment: rents, upkeep and maintenance, utilities, etc); a program's overhead likewise is the physical place where its work gets done, the computer and all of its associated resources (memory, CPU cycles, bandwidth, etc).
You are referring to the word in two different forms.

Overhead as a business cost is a ***noun***.
Overhead as in 'Birds flying overhead' is an ***adverb***.

More [here](https://en.wiktionary.org/wiki/overhead#Etymology_2)