What are the specific rules impacting how much war weariness is applied to each city?

The Civopedia doesn't provide much information on how "war weariness" relates to location except to say that it is applied to every city you own, and that it is greater when fighting occurs in foreign territory.

There seems to be something more to it though. I've been defending successive invasions from a couple of other civs, and 4 of my cities have 0 war weariness, and one has -6 war weariness. The city around which most fighting occurred has 0 war weariness, the next closest city has -6 war weariness, the two others on the same continent have 0, and a city on another continent has 0.

While I say I've been "defending," much of the fighting happened within range of a nearby city owned by the opposing civ (the cities are only a few spaces apart), so some of this could be considered foreign fighting.

This looks more like a fluke than a game mechanic because there's nothing special about the city with -6, but I could be wrong.

To summarize the wiki,

• Territory - Battles in your own territory accumulate less war weariness.
• Type of War - Surprise wars accumulate more war weariness than casus beli declared wars.
• Ghandi - His trait increases the war weariness of anyone fighting against him.
• Great Admiral - Joaquim Marques Lisboa causes you to gain 25% less war weariness when retired.
• Combat - Each turn at least one of your units is engaged in combat (attacker or defender).
• Death - Losing a unit will increase your war weariness.
• Nukes - Firing or being targeted by one will increase your war weariness.
• Pillaging - Having your tiles pillaged.

Other notes

• Peace - Naturally decreases war weariness each turn that you are at peace.
• Passivity - Not engaging in combat (no units whatsoever) on a turn will not increase your war weariness that turn even if you are at war (unless other factors above apply).
• Capturing a City - Capturing or having your city captured does not affect war weariness (including razing). These are purely diplomatic actions.

My Thoughts

• Take a Pause - If you're having weariness issues and you're the aggressor in the war, it might be a plausible idea to take a pause so you can address your amenity problem before continuing with your aggression.
• Capturing - Capturing a city makes it yours (duh) which means your units might be fighting in your territory which doesn't increase your war weariness as much.