Righteous deeds in Makkah are better than those done elsewhere, but we do not know to what degree they are better, except in the case of prayer

It is not saheeh; it is a da‘eef (weak) hadith that is not soundly narrated. Rather what is proven mentions the prayer only; one prayer in al-Masjid al-Haraam is equivalent to one hundred thousand prayers offered elsewhere, and one prayer in the Mosque of the Prophet (blessings and peace of Allah be upon him) is better than a thousand prayers offered elsewhere. As for fasting, there is no proven report about it, except for a da‘eef hadith which says that it [fasting Ramadan in Makkah] is better than one hundred thousand elsewhere. But it is da‘eef (weak). However, righteous deeds have a special virtue when done in Makkah; fasting, giving charity, reciting adhkaar and other righteous deeds have a special virtue. But there is no evidence to prove the degree to which they are better (than righteous deeds done elsewhere), apart from prayer. End quote.