Correct spelling, explanation: for many learners of English the form being sounds strange, but it is just a gerund form that occurs when we add -ing to the verb -be. The original form of the verb bēon comes from Old English and later, through centuries, it evolved into the form we know today.

Definition of being:
1. noun – a person, thing, or state that exists,
I will never understand that boy, what a strange being he is.
2. gerund form – added to a verb -to be,
I really enjoy being home on my own.

Expressions with being:
The word being appears in a few commonly used expressions, these include:
1. human being – a person,
My grandmother is such a lovely human being.
2. well-being – being happy and healthy,
My well-being is the result of everyday exercise and a healthy diet.

Idioms with being with being:
1. for the time being – for now,
For the time being, we just need to stay calm and wait for the test results.
2. with every fiber of your being – it means you want something or believes in something really passionately,
He wants to complete his first marathon with every fiber of his being.
3. all things being equal – as expected,
All things being equal, I should finish the project in two days.

Incorrect spelling, explanation: it is difficult to say why, but users of English tend to double the letter -e while adding the -ing ending to the verb to be. The form beeing, however, is wrong and rather refers to a common insect than to the verb -be.

Incorrect spelling

Incorrect spelling