All measurements are relative to a unit. The unit is defined for a purpose. If your planting crops you only need to know what month it is. If you have an appointment you need to know what hour it is. If you are
performing an experiment in a labratory you might need a laser frequency. The point is they are all
sufficient for the purpose. The choice depends on the expected duration of the activity. The closest consistent
periodic process we are aware of at present, is light transmission. Because light is fundamental to perception
of the world and energy exchange at the atomic level, it would seem to be a good choice as a reference for
measuring time, thus its involvement in relativity theory. As already mentioned, our common experiences
don't involve the extremely small ,or large, or fast. In our own ignorance of how the world really works,
we use trial and error methods until we gain some understanding. The tendency is to assign the common
properties of everyday experience by extrapolation to the unknown areas. As for the world being weird,
the world works the way it is supposed to work, it may be the properties that we assign to things that are
weird. As for the clocks, experiment proves they run slower. This is the result of comparing the motion of
the clock to the motion of a light photon.