Is it permissible for pilgrims to depart Muzdalifah after the middle of the night?

Spending the night in Muzdalifah is an obligation according to the majority of the scholars. This obligation is accomplished by staying for just a brief moment after the middle of the night. This is because the pilgrim would have spent more than half of the night there, thus it is accurate to say that the pilgrim spent the night there – though it is recommended for him to spend the entire night at Muzdalifah until he has prayed the Morning Prayer. He would then stop at al-Mash‘ar al-Haram1 to supplicate Allah until sunrise, and then proceed to Mina to stone Jamrat al-‘Aqabah.
It has been reported in a hadith that the Prophet permitted women, weak individuals, and those who have an excuse to depart from Muzdalifah after the middle of the night in light of their circumstances and to alleviate their hardships. Anyone who finds hardship in crowding may do the same.
Ibn ‘Abbas said:
I was one of those whom the Prophet sent early during the night of Muzdalifa, since I was among the weaker members of his family. [Bukhari]
And Allah Knows best.