How do humans perceive height or vertical drop?
The answer that I recently discovered is that humans have a number of mental adaptations to environmental challenges, as described by Evolutionary Psychology. 

For example, This TED talk on beauty describes how most "beautiful" landscape paintings share common traits, like looking down a valley with wildlife, a water source AND gravitational advantage (as if looking down from a tree).

The explanation given is that gravitational advantage (being higher) helps evade predators and spot them as they approach. 

From looking at these adaptations, it appears that there's neural circuits in the human brain which can recognize height and prefer it in some amount (as in sitting in a tree), but feel aversion towards it in greater amounts (staring down a cliff).