I'm not sure what you mean.
I just loaded up one of my 'Always War' games (turn 288) and I don't see any war weariness.
Obviously, there would be plenty of time to get it by then.
Look at each of your cities under the happiness section. If you don't see any reaction from your people regarding the war, then you don't have it either.
If you are referring to the reactions from ther AIs such as the comment, "This war spoils our relationship", then I wouldn't worry about it. Those will always be up there for the entire game, because you are at war with them for the entire game.
If it doen't have an effect on your cities, then it doesn't really matter. You can still go on building up your cities and building units to defeat them.
Some other notes regarding 'always war'.
Don't bother with buildings, civics or wonders that effect war weariness, since they have no effect.
Since, you can never trade with an AI, you might want to turn off tech trading and tech brokering as they will only help the AIs.
Also, mercantilism becomes more attractive, since you don't have foreign trade routes to lose.
Worker stealing becomes essential to slowing down the AI's economy. Delay them from building farms, roads & other improvements, pillage the rest and you easily overcome them. Woods2 promotion will permit you to quickly grab workers. Rotate out your units to keep gaining xp for their replacements.