Does compassion and mercy disappear from a person towards the weak and the poor when thinking rationally that God is more merciful to them, and that tribulation is for a reason and a mercy, even though helping is required to earn reward?

This way of thinking is incorrect. Allah tests His servants to see the mercy in their hearts. Showing mercy to those afflicted is a more perfect state than not showing it. This was the state of the Prophet, peace and blessings be upon him, who wept at the death of his son Ibrahim out of mercy and compassion, while also being content with Allah's decree and thanking Him. Ibn al-Qayyim clarified that the Prophet, peace and blessings be upon him, combined contentment with Allah's decree and mercy for his child, whereas the gnostic (arif) who laughed at the death of his child had a heart too narrow to combine the two matters. Helping those afflicted and showing them mercy is rewarded. Perfection lies in combining submission to Allah's judgment with mercy for the creature, based on the Prophet's saying, "Be merciful to those on the earth, and the One in the heaven will be merciful to you."