You both are correct - war weariness does take a few rounds to kick in, and it does return quickly if you make peace and then go to war again.
Here's an interesting qurik - with militaristic Civs, I've discovered that in a Republic/Democracy, war can actually cause happiness, and peace can end it. I believe it was a confluence of circumstances - I had three or four armies in the field and a decent set of units to complement them; I had a distinct advantage over my opponent and a chance to wipe them out. So I started fighting, captured my "key" cities, and made peace. My core cities actually ended their celebrations. When I redeclared war after a city flipped, everyone became happy again (that is, except those nationals of my opponent. I know I had no police stations, but I think I had constructed Universal Suffrage.
An additional point - with militaristic Civs + Heroic Epic, you can really crank out Great Leaders with a little luck. Try jumping right to Infantry in the Industrial Age and then goading the weak enemy with longbowmen to attack you - your infantry will be near invincible and you have a good chance of getting a leader or three.