I think that you are referring to the power ranking, and to the influence display.
The power ranking is mostly about military power. The simple way to increase it is to make more troops, level your heroes or upgrade your existing troops. The best way to shift the power balance it is to destroy the AI's armies and occupy the AI's cities.
I have to also say that I do not believe much in defensive armies, except in at most one city per ongoing war. When the enemy armies come knocking, destroy him. Once he enters your dominion, he will be slowed down to one tile per more, and you can further reduce that by casting "Tremor" and "Freeze" on him so that your reaction force can intercept him.
So consolidate your forces, make sure you have enough to defend your borders, get all your best heroes and troops in a big army, and take the war to him. Occupy cities, and do not worry about garrisoning defenders in them or suppressing the unrest. Make sure you flip all the outposts around them, though (to slow down the enemy)
The AI will see weak cities, send an army, and you will use your higher mobility (because it's your dominion now) to intercept them with your best army. Once he stops sending more than a trickle to attack, take another city, and repeat until he has nothing you want.
Then broker peace, make him sign trade and technology treaties, and in a few turns ally with him. A vassal is better than a dead enemy in this game.