Even our "direct" perceptions, such as of how much a box weighs, are greatly influenced by our expectations. From a recentNew Scientist:
Get hold of two cardboard boxes of different sizes and put a brick in each one. Check they weigh the same, then get somebody to lift them and tell you which is the heavier. The vast majority of people will say that the smaller box is heavier, even though it isn't, and will continue to maintain that it is even after looking inside both boxes and lifting them several times. … Curiously, experiments show that even though people initially use greater force to lift the larger box than the smaller one, on subsequent lifts they unconsciously equalise the amount of force they use to lift them. Despite their bodies apparently "knowing" that the boxes weigh the same, their minds still perceive the smaller box as being heavier. …
[Someone] showed that we can unlearn the size-weight illusion. He got volunteers to spend several days manipulating boxes that became lighter the larger they were. At the end of the process he found that their size-weight illusion was reversed. … This is good evidence that the illusion arises out of experience of the world, where larger objects tend to weigh more than smaller objects of the same kind.
This makes me more forgiving of people whose mistaken beliefs are contradicted by evidence right "before their eyes." Our eyes don't see nearly as much as we'd like.