Reference: Fataawa al-Hajj wal-‘Umrah waz-Ziyaarah – Page 76
Question: The one who is performing the sa’ee or tawaaf carrying a small child or someone who is ill, is he rewarded for the sa’ee and tawaaf along with the one he is carrying or not?
Response: The one who is carrying is rewarded for his intention, and the one carried is rewarded for his intention so long as all his faculties are sound. This is the most correct of the two opinions amongst the scholars.
And with Allaah lies all success and may Allaah send prayers and salutations upon our Prophet (sal-Allaahu ‘alayhi wa sallam) and his family and his companions.