If you hover the cursor over your XP bar in the top left, it will give you a full breakdown of exactly what kind and how much xp is needed to level up as raider or antagonist. It's about as clear as it can get, in that regard, but if you want the short and sweet: if 20% of your XP to level is as an antagonist, you level up as antagonist.
Aequilibrium moves every time someone in your randomly generated list of players levels up. Leveling as a raider moves it to the left, leveling as an antag moves it to the right. Seems simple to me, but I am not sure how you get grouped up, as my grouping has changed some times.