what is the trick to go to war with republic? i cant stand the war weariness.
Win. Don't lose cities. Either fight smart enough to lose few units or keep the war short. Time in a war is a factor, but losing many units in foreign conquests and losing cities to enemy civs really cranks the weariness sky-high.
For an effective short war, have a goal. I am usually trying to grab a new resource or monopolize a resource, but sometimes I am capturing a wonder or capturing a specific area, say to consolidate my border land lines. After the objective is achieved, end the war and either find the next war or build up appropriate infrastructure.
However there are occasions where I don't have appropriate infrastructure to build, so I keep building units, rolling over the enemy and cranking the lux slider as needed because I have nothing better to build, and I might as well build the destruction of my enemies!
Know what affects your weariness. If the enemy gets another civ to declare on you, be aware that you get war happiness as your citizens rally to support their civ. Further be aware that happiness goes away as soon as you make peace with that civ, so sometimes you might increase the effective war weariness by ending a war! (Clarification: If a civ declares on you for any reason {edit: Lanzelot corrects this below} you get some war happiness, and when you end the war with that civ that war happiness goes away. It doesn't make a difference if their declaration is due to an MA or MPP or just AI jerkiness.)
Oh, also know that war weariness is per-civ and wears off after 20 turns, so alternating wars is a great way to minimize weariness.