When a load is placed on the head, there is a lot of stress/pressure/force on the head. So the muscles feel compressed. So the muscles fell the pain.
We do not see much of bending of the muscles. But, they do get pushed in a little. Truly speaking the body does some work. Like a spring gets compressed. So we do spend some energy.
However, as per the law that work = force * distance,,
If we say that the load is not moved vertically, then the work done is zero.