What happens when two objects with different masses collide?

if the colliding objects have unequal mass, they will have unequal accelerations as a result of the contact force that results during the collision.

The object with the bigger mass will most likely push the smaller one back or if their big enough the big one will obliterate the small one (take a smart car going head on with a semi for example). unless it's something like a weather balloon vs. a car, then the balloon would have the bigger mass and the car would be smaller mass, but it would still push back the weather balloon.