How is momentum conserved when the big rolling ball hits the smaller rolling ball?

It balances out. When two objects collides, momentum is always conserved. Newton's Third Law...
This will also mean that Kinetic Energy is equal to the forces present in the collision. Meaning that Kinetic energy isn't conserved, but momentum is. 
In this case, the two objects involve a smaller and larger one. The smaller ball wouldn't have had any momentum to start with. Why? well think about the formula for momentum.
P = mv
Assuming, that the velocity of the impact is the same for both, we need to consider the mass of both the objects. Because the smaller ball has a smaller mass, it will have less momentum than that to the larger ball. The Larger ball will transfer its momentum to the smaller ball in collision. 
Try out an experiment, see the results, that should help you. Analyze carefully how each ball reacted. 

I hope this helped :)