@Ali has mentioned the social political connections, but I would like to elaborate more: It has come partly from here but it is in Persian.
Your question is basically why god has let the Prophet marry Aisha?
The answer is that it has been for political reasons. The prophet (pbuh), to reach better status socially and politically, in order to advertise and spread Islam as much as possible did some marriages. Here I list them and explain more:
- Aisha: The daughter of Abubakr from the tribe Tim (Quraish)
- Hafsah: The daughter of Omar from the tribe Edi (Quraish)
- Om Habibah: The daughter of Abusufyan form Bani Omayah (Quraish)
- Om Salamah from Bani Mahzum
- Meimunah from bani halal
- Safiah from bani israil
Sorry for the transliteration of Arabic names :)
As you see all of them are from different tribes. Back then marriage was the primary element to strengthen the relations between different tribes. Marriage to a different tribe was the number 1 element to avoid wars between different tribes (ref. Ibn khaldun introduction)
For this reason the Prophet (pbuh), tried to marry women from different tribes, even from Bani omayyah to decrease their aggressiveness toward himself, creating love possibly, and better spread of Islam.
Quote from La vie de Mahomet from Georgio:
We read in some historical books that the Prophet (pbuh) proposed
several women, and He did not even marry them all, but even this much
the whole tribe was honored and it created a good relation between the
Prophet (pbuh) and that tribe. For example when Umm Salamah from bani
mahzum (the tribe of Abujahl and Khalid ibn valid) married the
prophet, Khalid enemity towards the Prophet (pbuh) lessend very much
and after not so long he embraced Islam. Another example is Juirieh
and Safieh, which caused the calm down of Bani nazir and bani mutlaq.
For the marriage of Juirieh with the Prophet (pbuh), the sahabah
released 100 captives of war since they became relatives with the
Prophet (pbuh).
Also note that all these marriages happened after Hazrat Khadijah in the final years of the Prophet, since the Prophet wanted to be sure of the love between the different tribes which were really enemy before. Therefore, don't be under this impression that Aisha was any better than other wives of the Prophet.
For example in Surah tahrim verse 4, God speaks about the mistake of two wives of the Prophet (pbuh):
إِنْ تَتُوبَا إِلَى اللَّهِ فَقَدْ صَغَتْ قُلُوبُكُمَا وَإِنْ
تَظَاهَرَا عَلَيْهِ فَإِنَّ اللَّهَ هُوَ مَوْلَاهُ وَجِبْرِيلُ
وَصَالِحُ الْمُؤْمِنِينَ وَالْمَلَائِكَةُ بَعْدَ ذَلِكَ ظَهِيرٌ
If ye two turn in repentance to Him, your hearts are indeed so inclined; But if ye back up each other against him, truly Allah is his Protector, and Gabriel, and (every) righteous one among those who believe,- and furthermore, the angels - will back (him) up.
Next verse:It may be, if he divorced you (all), that Allah will give him in exchange consorts better than you,- who submit (their wills), who believe, who are devout, who turn to Allah in repentance, who worship (in humility), who travel (for Faith) and fast,- previously married or virgins.
Sahih Bukhari (صحيح بخاري کتاب فرض الخمس باب ما جاء في بيوت ازواج النبي صلي الله عليه وسلم):
حَدَّثَنَا مُوسَى بْنُ إِسْمَاعِيلَ حَدَّثَنَا جُوَيْرِيَةُ عَنْ
نَافِعٍ عَنْ عَبْدِ اللَّهِ رَضِيَ اللَّهُ عَنْهُ قَالَ قَامَ
النَّبِيُّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ خَطِيبًا فَأَشَارَ نَحْوَ
مَسْكَنِ عَائِشَةَ فَقَالَ هُنَا الْفِتْنَةُ ثَلَاثًا مِنْ حَيْثُ
يَطْلُعُ قَرْنُ الشَّيْطَانِ
The prophet points to the house of Aisha, and repeats this sentence three times: Fitnah is here, here is where the Hizb of Satan will appear.
In conclusion, you should read history unbiased and see what happened and what the consequences were. Aisha was among the other wives of the prophet, which apparently did several mistakes including the well-known battle of camel. I doubt if anybody can deny that. I am very worried that when I speak about this sensitive issue one of the Sunni brothers gets angry. Nevertheless, the wives of the Prophet are Umm Almuminin, which means that nobody can marry them after the Prophet.
EDIT:
I want to add some text about an issue that came up in the comments of @thecorocodile... answer. Basically the questioner is asking, why God that knows about the future and he is all wise and all knowing, why should he let his Messenger (pbuh) do sth which can be potentially wrong (in this case marriage with Aisha)?
Note that as mentioned in this answer, there were a lot of benefits through the multiple marriages of the Prophet (pbuh). It may only seem wrong because of the things that are mentioned in the question which are true indeed. But this conclusion (wrong decision by Allah) is subjective. Proof needed to support the argument. Sometimes we don't comprehend the reasoning behind things from the beginning. I suggest you read this. It might help a lot.
And God Knows best,
Hope this helps,
PS: For the age of Aisha when she married the Prophet (pbuh), see this at least. Neither 6 nor 9 seems to be true.