I don't know but my speculation:

• Europe's economy (from which the Church's income was largely derived) didn't go into overdrive until the Renaissance / Columbus landing in America.
• That growth being offset by the Reformation, with a lot of Europeans leaving the Roman Catholic Church.
• The somewhat decentralized nature of the Church, with a lot of assets in the hands of monastic orders and semi-autonomous archbishoprics.
• Perhaps an absolutist theocratic monarchy is not the most conducive form of government for economic and population growth.

The population started to tick up with the Renaissance, but when Italy essentially unified under a more modern constitutional monarchy in 1861, ending the Pope's temporal power over the city, Rome's population growth went stratospheric.

Source: https://www.jetpunk.com/users/quizmaster/charts/population-of-rome-over-time