If one is at War with another CIV and does not have casualties, War Weariness does not affect the population as it does when the War is Not going well and units are being lost. I have played many games with no real War Weariness due to fewer losses.
Not having War Weariness or rather the Signs of it when the Cities are celebrating WLTK Day is from the population being Happier. When a City is celebrating WLTK Day, it is a result of the Player handling all things where the Population is Happy and this includes how the War is handled.
The fact that War Weariness is possible is there but how one handles the Happiness of the Population during Wars has a direct affect on the results of it. It is Not that War Weariness actually is removed but rather not experienced.
All of the things a player does to gain Happiness for the Population counters discontentment and if the majority of the Population is Happy, War Weariness is not generally experienced. Especially if the player does not have losses and the War is going well where the Player is winning in battles and gaining Cities rather than losing them.
If a Population is Happy and at War with no real losses but rather positive Gain, why would a Population have Any War Weariness?
WLTK Day is celebrated because the Player has handled all things where the Population is Happy. If at War and the Player is Winning rather than losing, has little or no loss and keeps the Population Happy, War Weariness is not experienced.
A Golden Age helps to lessen War Weariness, especially when the Player continues the Happiness of the Population and handles Wars in a manner that is positive rather than negative.
Try losing units and Cities when at War and don't bother trying to keep the Population Happy with Luxuries or anything else, then see how fast War Weariness takes place
A Golden Age and WLTK Day are two different things. A Golden Age is an Age of Prosperity for an entire Civilization where the things a Player does for the Happiness of their Population has Greater impact. This Age is set for a specific amount of time. WLTK Day is a Reflection of the Happiness of a size 6 or above Population in any City and at any time due to the things a Player does to make a City Population Happy as well as prevent Unhappiness.
If a Player has Cities celebrating WLTK Day, he has already handled those Populations in a manner that caused them to be Happy, so this is an "indicator" that he is handling the Population well. IF at War, he must obviously be handling it well or the Population would not be Happy. This differs from going through a Golden Age of prosperity that positively affects the Mood of the entire Civilization and is set for a specific amount of time.
Neither a Golden Age nor WLTK Day removes the possibility of War Weariness... A Golden Age simply allows a Player an easier time keeping their People Happy and avoiding War Weariness while WLTK Day in a City is an indicator that a Player is doing it.