Why are some neighborhoods called "heights?" Is it a reference to elevation or location?

If you type your question into google.com you get several pages of the history of Brooklyn, but they never say anything to answer the question.

I would guess it's because people like to think of high places rather than low places. For example, every city in the world has the rich neighborhoods on the north side and poor neighborhoods on the south side. Except one: La Paz, Bolivia. That is because La Paz is on the side of a mountain and the south side of town is above the north side, and people really prefer to look over their less prosperous neighbors. So the higher property values are on the south side: the higher side.

Example #2: The one place in the USA with the worst reputation is called "Washington, D.C." It is also called "Foggy Bottom".