It's easy to produce this sensation by covering one eye for a half-minute or
so - the covered eye adapts to the dark and for a little while sees things
"brighter".

When it -is- a sign of problems, it's often the color red that is most
affected.

Look at something colored primary red, against a white background,
alternately with each eye. If it looks pale or washed-out with one eye, see
a doctor soon. If they're both the same color red, it probably isn't a
serious problem.

These problems often affect the behavior of your pupils, too.

-MT

Can be a sign of asymmetric optic nerve disease/conduction.

It can be something as benign as relative optic nerve hypoplasia or
something as serious as a tumor.

If this is something acute, I would recommend you get your eyes
checked.

Have a look in the mirror.  Is your right eye's pupil wider than your
left eye's pupil?

Use a flashlight and try to watch how fast each eye responds to the
light.

What you describe is what I would expect if your right iris were lazy
or impaired somehow.

Since wearing contacts (which means I spend a lot more time looking at
my eyes in the mirror), I've noticed that my right pupil is always
larger than my left pupil.

I'm reasonably sure I've noticed a difference in brightness while
reading in bed without corrective lenses, which I would now attribute
to the difference in pupil size, but I'm not entirely certain.  Since
my relaxes focus is about 10 inches from my eyes, I tend to cover one
eye while reading, to avoid making my eyes work at converging on the
text (though I sometimes just don't let them converge and read from
one of two text images).  When switching which eye is covered, the
newly-uncovered one will be dark-adapted, and hence see things as much
brighter.

It's difficult to remember if I ever had both uncovered long enough to
kill all differential dark adaption while still noticing a different
perception of brightness.

In any case, I don't know how unusual it is, but I wouldn't be
surprised if a large number of people have asymmetric pupil sizes to
one degree or another.