Weight and Cosmic Love

This ring does not weigh anything,
the needle does not move from zero
and I cannot make it show
even a milligram.
Your husband must be alive—
in which case neither of your rings, taken separately,
will weigh anything—only both together will register.

Karol Wojtyla, The Jeweler's Shop, act II

What if it were a cosmic law, and not only a law of love, but a physical law that the each member of a couple separately lacks the significance of the pair together?

We cannot know directly whether unpaired charged lack weight. The problem is that electromagnetic forces are so large that only the smallest particles are tolerated to remain unpaired for any significant time, and these are too small to have appreciable weight. Put another way, the systematic uncertainties of electromagnetic forces so far dominate gravity as to make the latter completely negligible.

But are there indirect ways to know whether unpaired charges lack weight? What would the universe look like were this true? Would it differ from our own? If so, how?