Civilization – Does the warmonger penalty go down over time

The Civilization VI ‘Fall 2016’ seems to have changed how the Warmonger penalty works:

"Reduced Warmonger penalties in most instances, and adjusted how this reacts to returning versus keeping a city. The last city conquered from a player now provides a heavy warmonger penalty, even if you have a Casus Belli against this player, because you are wiping out a civilization."

and

"Players will no longer receive any warmongering penalties from a joint war partner for actions in that joint war."

https://civilization.com/news/entries/civilization-vi-fall-2016-update-now-live

There's no upper limit on the number of cities you can have in Civ VI. However, your Amenities gained from Luxury Resources can only give a bonus to four cities (six for Aztecs), so every city created beyond the fourth will reduce the Amenities available in each city. Since Amenities impact how productive your cities are you'll want to avoid expanding too fast if the Amenities in your cities are already fairly low.

Other than concerns about Amenities though there really isn't much of a negative to founding more cities, and you'll usually get some benefit from every city you create.