Hmm. I get this too, that's why I haven't yet finished a game, yet have started about 5. Perhaps try something REALLY implausible like invading a small city on another continent and NOT losing it to culture long enough to march a gratuitously large force there and sweep the place.
It seems to me inevitable that this weariness will set in unless you are fighting from behind, fighting for a special resource, politicking to start wars or invoke a war for the hell of it. A kind of "no-war weariness", I guess.
So, war is necessary for the later game - WHAAAT?! I said, war is neccessary for the later game. Cut through them like a Japanese Buzzsaw and see how many will become "just another victim".
Hell yeah!