Answer:
The objects must have the same acceleration and the objects must exert the same magnitude force on each other.
Explanation:
The objects must have the same weight: FALSE. This is not needed, any two object can move together in contact no matter their mass.
The objects must have the same acceleration: TRUE. If they have different accelerations, they will separate since the distance each of them travel at a given time will be different.
The objects must have the same net force acting on them: FALSE. This is not needed, since what matters is acceleration, and a=F/m, so if both objects have different net force acting on them, they could have different masses also to compensate and result in the same acceleration.
The objects must exert the same magnitude force on each other: TRUE, this is the 3rd Newton Law, an action must follow the same reaction.