Well, Dr. Boom, for me it will depend on HOW war weariness is handled.
For instance, War Weariness (as a happiness penalty) should rise and fall according to changing circumstances. For instance, a defensive war should cause WW to rise at a MUCH lower rate than a war fought on the other side of the world (and wars to defend/liberate allies should also count as 'defensive'), and militaristic civs should gain WW at a lower rate than, say, commercial and agricultrual civs. The resources you put into 'internal security' should also effect WW accumulation (to reflect propoganda), as should your levels of Nationalism and/or Theism. Another factor which should effect war weariness, though, is VICTORY/DEFEAT. If you lose lots of battles, lose cities, or lose lots of conscript/regular forces, then WW will rise. If, however, you WIN lots of engagements, then War Weariness may actually go DOWN to the point of getting 'War Happiness'
!!
If War Weariness reduces happiness enough, then it should be a possible trigger for a civil war/rebellion!!
Yours,
Aussie_Lurker.