How is the equilibrium of 21% oxygen in Earth's atmosphere established?
I'm not sure I can give a good technical answer. I don't think the amount of oxygen in the Earth's atmosphere is due to equilibrium but more of a consequence of the formation of the solar system, Earth chemistry and biology.

If you look at the formation, for inner planets, much of the gas and ices were blown off due to their inner orbits and the planets being too hit by very active Coronal mass ejections in the early solar system. There are 3 likely types of close to the sun planets:   1) small rocky planets (Earth, Mercury, Venus, Mars), 2) hot jupiters, which are large enough to trap hydrogen even though they're close to the sun and hot and 3) super-earths, which have enough gravity to trap hydrogen.

An abundance of hydrogen in a planetary atmosphere would likely make oxygen formation impossible.  The Oxygen would bind with the hydrogen.

The Earth didn't have the gravity to trap much hydrogen and some of the early atmosphere would have been blown off by large meteor strikes and by coronal mass ejections, which were much more common when the sun was young.

A clue to the Earth's atmosphere's formation is the formation of the oceans, because oceans would be impossible without an atmosphere.  The oceans formed 3.8 billion years ago, so we had to have an atmosphere, at least for about 3.8 billion years.

http://people.chem.duke.edu/~jds/cruise_chem/oceans/ocean1.html

The young Earth's atmosphere was mostly methane (CH4), ammonia (NH3), water vapor (H2O), and carbon dioxide (CO2) as per the link above, as soon as the Earth was cool enough, the water vapour turned into liquid water (rain) and the oceans began to form.

Fast forward to the Great Oxygenation event when cyanobacteria, pulled CO2 from the air and release O2.  Early on, the O2 binded with iron in the ocean and some of it likely reacts with CH4 and NH3 in the atmosphere when there is lightning. Over time, CO2 was pulled from the air, replaced by O2 and O2 reacted with CH4 and NH3, producing more CO2, H20, and N2 - the common elements we have today.

Oxygen levels in planets with cyanobacteria, likely depends on how much iron is dissolved in the oceans and how much hydrogen is in the atmosphere.  If there's not enough CO2 to produce enough O2 to saturate the iron and hydrogen, the planet probably never gets much O2 in it's atmosphere - so it's all about the ratio of early elements.    Super-earths might never get oxygen atmospheres - too much hydrogen.

You also get factors like the development of lignin (got that from Neil deGrass' Cosmos) - http://evolution.about.com/od/Cosmos/fl/Cosmos-A-Spacetime-Odyssey-Recap-Episode-109.htm

Lignin made trees possible, but nothing could eat trees, so trees captured more and more carbon, so CO2 levels fell and O2 levels rose.   About 100 million years later, termites evolved and the digestion of trees released much of this captured CO2 became possible and Oxygen and CO2 leveled out.

Shellfish, to make their shells, take more O2 out of the air than CO2 (calcium carbonate has lots of oxygen in it).   That's a slow process, but over time it takes some O2 out of the air, so over tens of millions of years, parts of the atmosphere are effectively sequestered and trapped in the Earths crust, but over time, some of this is also returned to the atmosphere with volcanic activity - so the type of life forms present is also a factor and the extent of tectonic activity is a factor as is, as is the presence of a Jupiter and how many comets are likely to hit the planet and the size of the planet.

It's more chance, the solar system and planetary factors that lead to a planet's atmosphere.

To answer your question:  


  So if we increase the amount of oxygen, it will decrease over time and
  if we decrease it, it will be replenished.


Tough call regarding oxygen.   CO2 is easier.    Because there's a relatively small percentage of CO2 in the air, more CO2 will lead to some of it dissolving in the ocean as carbolic acid, though the warming of the ocean might also slow the oceanic absorption of CO2.     Because there's so much more Oxygen in the Earth, 21% vs 0.04% of CO2, a measurable increase, say 21% to 22%, you'd probably see a slight increase in dissolved O2 in the ocean, but beyond that, I don't think you'd see that extra oxygen go away any time soon.  My guess is, if such an increase was done, it would last a long time, hundreds of thousands of years if not millions, because oxygen sequestering is pretty slow.     Insects would get slightly bigger pretty quick.   That might be the most noticeable effect.  

If you significantly increase O2 levels, say from 21% to 30%, things would become noticeably more flammable and over time, our lungs would probably get smaller and there would be other effects, probably.    But I don't believe there's any sort of equilibrium that would fairly quickly bring it back to 21%.