Ok here are some stats from my game
It looks like every razed city add 1 to war weariness, and cities being razed may add 0.5. It also looks like every razed city is -5 to relations, and cities being razed may be -2.5.
Not sure about influence yet from these stats.
Modern Age | Epic | Sovereign | Standard Rules | Continents Pls
Map Random Seed 976474
Build 1.01 (1092363) Metal
Napoleon, Revolutionary
America
Elective Republic
I can confirm I do not have any Diplomatic points put into leader attributes.
Turn 130 October 1874:
Cities: 27/19
Qing - eliminated
Cities conquered and razed in this age: 17 | 15 razed | 1 being razed | 1 occupied
Happiness: Total (+93) Settlement (-1464) Other (+1557)
Influence: Total (-79) Settlement (+17) Other (-96)
Diplomatic actions: Ongoing Denounce Military Presence (Prussia), Open Borders (Russia)
Ideology: None
Turn 124 April 1871:
Cities: 30/19
Qing - eliminated
Cities conquered and razed in this age: 17 | 12 razed | 4 being razed | 1 occupied
Happiness: Total (+96) Settlement (-1705.5) Other (+1801.5)
Influence: Total (-78) Settlement (+18) Other (-96)
Diplomatic actions: Ongoing Cultural Exchange (Prussia)
Ideology: Communism
Turn 119 1868:
Cities: 29/19
Cities conquered and razed in this age: 16 | 12 razed | 3 being razed | 1 occupied
Qing War with Pachacuti -14 war weariness (Napoleon 3 / Pachacuti 17 /+14)
Relationship: -90 / -70 Razed a Settlement
Happiness: Total (+96) Settlement (-665) Other (+761)
Influence: Total (-34.5) Settlement (+70) Other (-104.5)
Diplomatic actions: Ongoing Cultural Exchange (Prussia)
Ideology: Communism
Turn 104 1853:
Cities: 30/19
Cities conquered and razed in this age: 11 | 6 razed | 4 being razed | 1 occupied
Qing War with Pachacuti -8 war weariness (Napoleon 3 / Pachacuti 11 /+8)
Relationship: -90 / -40 Razed a Settlement
Happiness: Total (+96) Settlement (-687.5) Other (+783.5)
Influence: Total (-10) Settlement (+81.5) Other (-91.5)
Diplomatic actions: Ongoing Steal Tech (Japan), Open Borders (Mexico), Cultural Exchange (Prussia), Denounce (Japan)
Ideology: Communism
Turn 92 1841:
Cities: 28/19
Cities conquered and razed in this age: 8 | 5 razed | 2 being razed | 1 occupied
Qing War with Pachacuti -7 war weariness (Napoleon 3 / Pachacuti 10 /+7)
Relationship: -90 / -35 Razed a Settlement
Happiness: Total (+102) Settlement (-597) Other (+699)
Influence: Total (+35.5) Settlement (+82.5) Other (-47)
Diplomatic actions: Recently ended Steal Tech (Qing) [this must have been at least a second time doing this] | Ongoing Cultural Exchange (Prussia)
Ideology: Communism
Turn 57 1806:
Cities: 27/19
Cities conquered and razed in this age: 5 | 3 razed | 1 being razed | 1 occupied
Qing War with Pachacuti -2 war weariness (Napoleon 3 / Pachacuti 5 /+2)
Relationship: -85 / -20 Razed a Settlement
Happiness: Total (+102) Settlement (-512) Other (+614)
Influence: Total (+67.5) Settlement (+92.5) Other (-25.5)
Diplomatic actions: Recently ended Steal Tech (Qing) | Ongoing Cultural Exchange (Prussia)
Ideology: None
Turn 36 1785:
Cities: 27/18
Cities conquered and razed in this age: 4 | 2 razed | 1 being razed | 1 occupied
At peace but 11 turns until able to declare war after making peace with Qing
Relationship: -90 / -15 Razed a Settlement
Happiness: Total (+87) Settlement (-468) Other (+555)
Influence: Total (+79.5) Settlement (+74.5) Other (+5)
Diplomatic actions: Recently Ended Declare War (Qing), Open Borders (Mexico) | Ongoing Military Aid (Mexico), Open Borders (Mexico), Open Borders (Japan), Open Borders (Russia), Befriend Independent (Swiss)
Ideology: None
Turn 8 1757:
Cities: 25/17
Cities conquered and razed in this age: 0 | 0 razed | 0 being razed | 0 occupied
At peace
Relationship with Pachacuti: -25 / 0 for razed a settlement
Happiness: Total (+105) Settlement (-467) Other (+572)
Influence: Total (+51.5) Settlement (+21.5) Other (+30)
Diplomatic actions: Ongoing Denounce Military Presence (Prussia), Open Borders (Russia)
Ideology: None
Cities I razed in my war with the Qing:
Apalachee - razed by turn 36
Anshan - razed by turn 36
Ulaangom - being razed in turn 36 | razed by turn 57
Qaraqorum - being razed in turn 57 | razed by turn 92
Aurag - razed by turn 92
Creek - being razed in turn 92 | razed by turn 104
Choctaw - being razed in turn 92 | being razed in turn 104 | razed by turn 119
Beijing - (may have been being razed, but recaptured by turn 92) | being razed in turn 104 | razed by turn 119
Houma - being razed in turn 104 | razed by turn 119
Altai - razed by turn 119
Guangzhou - razed by turn 119
Lanzhou - razed by turn 119
Cahokia - being razed in turn 104 | being razed in turn 119 | being razed in turn 124 | razed by turn 130
Khuduu Aral - being razed in turn 119 | being razed in turn 124 | razed by turn 130
Indrapura - being razed in turn 119 | being razed in turn 124 | razed by turn 130
Khuree - being razed in turn 124 | being razed in turn 130
Changsha - Not sure it seemed to disappear, maybe a city state razed it.
Burgi Ereg - Occupied by turn 36
Suzhou - captured by Caesar
@Calcifer @Morgawr
EDIT: I slept all my units and ran it to turn 147, and the other value for Influence stayed at -96, so it doesn't seem to revert to the mean over time.
I also learned you can never have a negative gold balance, and you cannot disband more than 1 unit per turn due to lack of gold.