Burden refers to an unpleasant considering pattern that does not arise from actual, passive desire to consider, but instead arises from a need to consider something a person wouldn't wish to consider. A child on the back seat of a car, constantly asking "are we there yet?", could be an archetypal instance of a burden.
The actuality of a burden is that the natural reaction of a stressed parent might be to tell the child to shut up in an unkind way, yet the effort required for not doing so isn't perceived to have potential for leading to an outcome that is somehow nice. The parent merely experiences a need make an effort not to be aggressive towards the child.
The behavior of the child is arbitrary in the sense that repeating the question does nothing to advance the journey. However, it could also be interpreted as expression of boredom. But arbitrarity can manifest anywhere, even in clothing. Suppose a person dresses up as a clown but would behave in an usual manner. That, too, would be arbitrary unless a reason for such a choice were found.
Arbitrary burdens often manifest via people who seek attention for the sake of attention itself.