being

being + adjective

We normally use the progressive form with an adjective when we are talking about actions and behaviour. And being unfair in your example sentence, Boon and Nukoon, relates to somebody's behaviour of not being fair in their actions, so the progressive form is preferred. Here are some further examples: 

• You're being silly / foolish / childish when you do such silly / foolish / childish things.
• I was walking on tiptoe and being very careful not to wake the baby.

However, when the adjectives relate to feelings, we do not use the progressive form:

• I was upset / worried when I heard that they would have to operate on John's knee.
• I am delighted / overjoyed to hear that you have passed all your exams.

being + past participle

We use being with the past participle, Bhavin, in present progressive and past progressive passive forms. So we might say:

• My car is being serviced. Instead of: The local garage is servicing my car.
• The computers are being installed tomorrow.
  Instead of: They're installing the computers tomorrow.
• My nieces enjoyed being taken to the circus.
  Rather than: I enjoyed taking my nieces to the circus.
• I was quite sure I was being followed.
  Instead of: I was quite sure someone was following me.
• She was being punished for being cruel to the cat.
  Rather than: They were punishing her for being cruel to the cat. 

Note that cruel in the above example is an adjective describing behaviour so the progressive form is used with it.

Note that other passives with being, i.e the future progressive passive (will be being) and perfect progressive passive (has been being) are quite rare.

being in participle clauses

We can use an adverbial participle clause to express reason or cause as an alternative to a because/since/as clause. Using a participle clause in this way is more characteristic of written English or a literary style, rather than spoken colloquial English. Compare the following:

• Being French, he is passionate about wine and cheese.
  Instead of : Because he is French, he is passionate about wine and cheese.
• Being a friend of Tony Blair, I'm often invited to No 10.
  Rather than: As I am a friend of Tony Blair, I'm often invited to No 10.
• Being quite slim, I was able to squeeze through the hole in the railings. Instead of: Since I am quite slim I was able to squeeze through the hole in the railings.
• Being rather over weight, Geoffrey was unable to squeeze through. Rather than: Because he's rather over weight, Geoffrey was unable to squeeze through.

verb + verb-ing / adj + prep + verb-ing

Note that being as verb-ing, is required in all such instances:

• Would you mind being quiet for a moment?
• I look forward to being interviewed on the current affairs programme.
• She was afraid of being accused of a crime which she did not commit.
• I am tired of being taken for granted and expected to do all the housework.