It is narrated from Sayyiduna Abdullah bin Umar (may Allah be pleased with him) that the Noble Prophet (peace and blessings be upon him) had permitted the weak people to leave Muzdalifah at night.
Benefits: … The honored pilgrims depart from Muzdalifah a little before sunrise, but those who are excused (ma‘dhur) are permitted to leave during the night, so that they may be spared the hardship of the crowd. However, there is consensus among the scholars that these excused individuals may not leave in the early part of the night. One should act upon the ruling stated in the first hadith of this chapter, that is, when one third of the night remains, at that time the excused individuals should depart from Muzdalifah.