Bismillah.
Volume 2, Book 26, Number 736:
Narrated Salim:
'Abdullah bin 'Umar (radiallaahu `anhu) used to send the weak among his family early to Mina. So they used to depart from Al-Mash'ar Al-Haram (that is Al-Muzdalifa) at night (when the moon had set) and invoke Allah as much as they could, and then they would return (to Mina) before the Imam had started from Al-Muzdalifa to Mina. So some of them would reach Mina at the time of the Fajr prayer and some of them would come later. When they reached Mina they would throw pebbles on the Jamra (Jamrat-al-Aqaba) Ibn 'Umar (radiallaahu `anhu) used to say, "Allah's Apostle (sallallaahu `alayhi wasallam) gave the permission to them (weak people) to do so."
Volume 2, Book 26, Number 737:
Narrated Ibn Abbas (radiallaahu `anhu):
Allah's Apostle (sallallaahu `alayhi wasallam) had sent me from Jam' (i.e. Al-Muzdalifa) at night.
Volume 2, Book 26, Number 738:
Narrated Ibn Abbas (radiallaahu `anhu):
I as among those whom the Prophet (sallallaahu `alayhi wasallam) sent on the night of Al-Muzdalifa early being among the weak members of his family.
Volume 2, Book 26, Number 739:
Narrated 'Abdullah (radiallaahu `anhu): (the slave of Asma' (radiallaahu `anhaa))
During the night of Jam', Asma' (radiallaahu `anhaa) got down at Al-Muzdalifa and stood up for (offering) the prayer and offered the prayer for some time and then asked, "O my son! Has the moon set?" I replied in the negative and she again prayed for another period and then asked, "Has the moon set?" I replied, "Yes." So she said that we should set out (for Mina), and we departed and went on till she threw pebbles at the Jamra (Jamrat-al-Aqaba) and then she returned to her dwelling place and offered the morning prayer. I asked her, "O you! I think we have come (to Mina) early in the night." She replied, "O my son! Allah's Apostle (sallallaahu `alayhi wasallam) gave permission to the women to do so."
Volume 2, Book 26, Number 740:
Narrated 'Aisha (radiallaahu `anhaa):
Sauda (radiallaahu `anhaa) asked the permission of the Prophet (sallallaahu `alayhi wasallam) to leave earlier at the night of Jam', and she was a fat and very slow woman. The Prophet (sallallaahu `alayhi wasallam) gave her permission.
Volume 2, Book 26, Number 741:
Narrated 'Aisha (radiallaahu `anhaa):
We got down at Al-Muzdalifa and Sauda asked the permission of the Prophet (sallallaahu `alayhi wasallam) to leave (early) before the rush of the people. She was a slow woman and he gave her permission, so she departed (from Al-Muzdalifa) before the rush of the people. We kept on staying at Al-Muzdalifa till dawn, and set out with the Prophet (sallallaahu `alayhi wasallam) but (I suffered so much that) I wished I had taken the permission of Allah's Apostle (sallallaahu `alayhi wasallam) as Sauda (radiallaahu `anhaa) had done, and that would have been dearer to me than any other happiness.
It is permissible for women to leave Muzdalifah before dawn, because the Prophet (peace and blessings of Allaah be upon him) allowed some women, especially those who were weak, to leave Muzdalifah after the moon had set at the end of the night. That was so that they could stone Jamarat al-‘Aqabah before it became crowded.
It is permissible to delay stoning the Jamrah until the night, if the woman’s guardian thinks that the crowding is too great around Jamrat al-‘Aqabah and that this may pose a danger to the women who are with him. So it is permissible to delay their stoning of the Jamrah until the crowding is less or has stopped, and there is nothing wrong with them doing that.
The same applies with regard to stoning of the Jamaraat during the three days of Tashreeq, when women can stone them after ‘Asr, which is the time when the crowding is a lot less, as is well known. If that is not possible then there is nothing wrong with them delaying it until the night.
More on rulings that apply to only women in Hajj here.
Taken from: http://ilookilisten.wordpress.com/2013/03/21/hajj-women-weak-ones-ahadith-1436-1441/
