I'd like to point out the parallel to the existentialist concept of "absurdity". From Wikipedia:

It is illogical to seek purpose or meaning in an uncaring world without purpose or meaning, or to accumulate excessive wealth in the face of certain death. Absurdity is used in existentialist and related philosophy to describe absurdly pointless efforts to try to find such meaning or purpose in an objective and uncaring world, a philosophy known as absurdism.

To draw out the connection: rather than saying "reality is weirdly normal", I would say: Reality is absurd in human terms. Physics does not care about you. 'Every action has an equal and opposite reaction' is not a principle of justice; it has only to do with kinetic motion. Conservation of energy does not entail survival after death. The universe is allowed to kill you. Physics will happily twist everything you find meaningful beyond recognition (including you yourself).

This has a depressing aspect which is not present in the post. Perhaps that is the largest flaw of existentialism. However, I think this concept of absurdity is valuable. "Absurd" takes things one step further than "weird", in a way I feel clarifies things.

Reality is absurdly normal.

=Edit=

The ensuing discussin has made me change my mind. The concept of the absurd is not an improvement here. Insisting that reality is absurd in human terms (strongly violating our intuitions and also our values) is not helpful; it's relevantly similar to insisting that life is a mystery or that quantum mechanics is impossible to understand.