does this have a huge effect on enemies, or is the point of getting SoZ purely to stop the +100% effect happening to you
How many? Is it worth enough soldiers to merit it over say...walls for such a purpose?
another thing to remember: when you capture the soz city, the ww halves in the same turn(as if they didn't have it at all from the start of the war).
Clearly war weariness accumulates quickly when a human player is at war with an AI that has the Statue of Zeus. But does SOZ have the opposite effect on an AI when the human player has SOZ? In my experience I rarely see AI's suffering significant war weariness even during long costly wars or at least it doesn't seem to mute their enthusiasm for continuing the war as it does a human's. I thus am skeptical that SOZ can be used offensively against AI's.
Mostly to prevent suffering from it. The AI has massive reductions to maintenance, unit maintenance, etc, and yes...war weariness too.
It isn't 100% insignificant on most difficulties though. If you rip 80 AI units apart in your territory it will hurt the AI in terms of WW, but that isn't the primary reason you'd be doing that.
Nine times out of ten though, the AI isn't suffering significant WW even if you'd be at 6or more.
How does Statue of Zeus help with wealth?