Some anecdotal observations from my games:
I've never had any war-weariness problems under Republic. I have had them under Democracy.
I can't be sure but it seams that taking losses also increases war-weariness. I have fought wars for 100's of turns to wipe out the big continent under Republic with no weariness, but I was using Mech. Infantry, Tanks, and Artillery against Riflemen and Cavalry. In another game I was fighting an equal-tech war under Democracy (and taking losses occasionally) and I eventually had war-weariness (didn't count the turns, sorry).
I found that the extra worker under Dem. is irrelevant because I prefer Industrious civs, and I measured the reduced corruption from Rep. to Dem. at 50 gold out of 1800 income per turn, not a big deal. So, my solution to war-weariness is to stay in a Republic. Only one government change in the whole game...
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I'm not giving in to security, under pressure
I'm not missing out on the promise of adventure
I'm not giving up on implausible dreams
Experience to extremes" -RUSH 'The Enemy Within'
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