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I've come across the following example sentences and I wonder why only one part of the sentence requires backshift when put into reported speech. I am familiar with the general rules as well as exceptions (still true, future ...) but I still can't come up with an explanation:

The pilot’s words were: ‘The weather was extremely bad as the plane came in to land.’

Reported speech: The pilot commented that the weather had been extremely bad as the plane came in to land.

was extremely bad -> had been extremely bad // plane came in -> plane came in

To me, both the weather and the action of the plane coming in to land are in the past.
Why don't we backshift the second part:
The pilot commented that the weather had been extremely bad as the plane had come in to land.

Or, what about this one:

Barbara said, “I didn’t realise it was midnight.”

Barbara said she hadn’t realised it was midnight.

Is it okay to say: Barbara said she hadn't realised that it had been midnight.

Thank you!

This goes to the distinction between tense and aspect: when you use an inflected form of have + [past participle], the primary marking is perfective aspect: you are saying that as of some time, a particular action being referred to had been completed, and its completion is relevant at the reference time of the matrix clause (i.e., the time of speaking or of reporting).

In this case, the weather being bad and the plane landing were things that were happening simultaneously, so perfective aspect is not appropriate. It would also clash syntactically with using the as + [clause] construction, which requires that the subordinate clause be able to take an imperfective reading. Compare the following two sentences (the asterisk means it sounds ungrammatical to me):

They had been shelling fava beans as Thomas came through the door.

*They had been shelling fava beans as Thomas had come through the door.

Finally, note that came in the subordinate clause is in its preterite form so a past time interpretation is there as needed for backshift.

It is all to do with tense simplification in subordinate clauses:

It should – logically – be

*The pilot commented that the weather had been extremely bad as the plane had come in to land.

but, because of tense simplification in the subordinate (time) clause, it becomes, as you noticed,

The pilot commented that the weather had been extremely bad as the plane came in to land.

Let me quote Michael Swan's Practical English Usage, Oxford University Press, second edition, fourth impression, 1996, page 583, entry 556, "tense simplification in subordinate clauses":

1 reasons for tense simplification

If the main verb of a sentence makes it clear what kind of time the speaker is talking about, it is not always necessary for the same time to be indicated again in the subordinate clauses. Compare:

This discovery means that we will spend less on food.

This discovery will mean that we spend less on food.

It is unlikely that he will win.

I will pray that he wins.

Verbs in subordinate clauses are often simpler in form than verbs in main clauses – for example present instead of future, simple past instead of conditional, simple past instead of past perfect.

You'll find Coca-Cola wherever you go. (NOT… wherever you will go.)

He would never do anything that went against his conscience. (More natural than… that would go against his conscience.)

I hadn't understood what he said. (More natural than… what he had said.)

If – like myself – you are not a native speaker of English, you must have noticed that in bilingual editions of books, the side which has the English version of the text is – nearly always – considerably shorter than the side which has the version in another language: the English version is much more concise than the version in a foreign language.

To me, this reflects a mentality – inbred, a question of nurture – characterized by a kind of abhorrence for redundancy: since "had been" establishes that the time the weather was such and such came before the time the pilot "commented" on it, and since the conjunction "as" establishes that the time the weather was such and such and the time the plane "came in" to land were contemporaneous, the speaker or writer feels they can do without a "had come in", sparing themself a word to pronounce or write!

In

"Barbara said (that) she hadn't realised that it was midnight."

unlike the conjunction "as" in your first example sentence, the conjunction "that" does not say anything about the time relationship between the two verbs in the reported clause, "realise" and "be", but the meaning of the verb "realise" does: "realising" is "being aware of something at the time it is happening"; so you do not need to go to the trouble of using a past perfect tense again, saying or writing "had been".

I have given such an answer already to the question entitled "I remembered seeing or having seem him?", which is also about tense simplification in subordinate clauses.