Sahih Muslim Book 7, Hadith Number 2965.

Chapter : It is excellent that the aged and the weak, especially among the women, should hasten from Muzdalifa to Mina at the latter part of the night before the people moving in multitude. and excellence of staying there for others until they observe the dawn prayer at Muzdalifa.

Ibn ‘Abbas reported: Allah’s Messenger (may peace be upon him) sent me from Muzdalifa ahead (of the caravan) along with the luggage or with the weak ones during (the latter part of the) night.