According to a number of narratives, Ayesha (ra) accompanied the Muslims in the battle of Badr and Uhud. Furthermore, it is also reported in books of hadith and history that no one under the age of 15 years was allowed to take part in the battle of Uhud. All the boys below 15 years of age were sent back. Ayesha's (ra) participation in the battle of Badr and Uhud clearly indicate that she was not nine or ten years old at that time. After all, women used to accompany men to the battle fields to help them, not to be a burden on them.
First, the prohibition applied to combatants. It applied neither to non-combatant boys nor to non-combatant girls and women. Second, `A'isha did not participate in Badr at all but bade farewell to the combatants as they were leaving Madina, as narrated by Muslim in his Sahih. On the day of Uhud (year 3), Anas, at the time only twelve or thirteen years old, reports seeing an eleven-year old `A'isha and his mother Umm Sulaym having tied up their dresses and carrying water skins back and forth to the combatants, as narrated by al-Bukhari and Muslim.
According to almost all the historians, Asma, the elder sister of Ayesha was ten years older than Ayesha.
Well, Ibn Kathir based himself on Ibn Abi al-Zinad's assertion that she was ten years older than `A'isha, however, al-Dhahabi in Siyar A`lam al-Nubala' said there was a greater difference than 10 years between the two, up to 19, and he is more reliable here.
It is reported in Taqri'bu'l-tehzi'b as well as Al-bidayah wa'l-nihayah that Asma died in 73 hijrah when she was 100 years old. Now, obviously if Asma was 100 years old in 73 hijrah she should have been 27 or 28 years old at the time of hijrah. If Asma was 27 or 28 years old at the time of hijrah, Ayesha should have been 17 or 18 years old at that time. Thus, Ayesha, if she got married in 1 AH (after hijrah) or 2 AH, was between 18 to 20 years old at the time of her marriage.