JJW,
My , (hopefully helpful), 2 cents:
You wrote "Measuring is something I can do but I never use a rubber tape."

That is exactly what relativity tells us to do, and
it defines just how, and in what direction to stretch
the 'tape`, both in time and space to make our
observations add up when we look from one set of
conditions, (frame), of gravity or velocity, to another.

It is against our instincts, but it agrees well with our observations to date.