IMO a skimmer is too big if it cant even force bubbles out of the neck. That means you have too few organics. the skimmer is too small if it keeps producing endless skimmate. people always say "my skimmer produces 4 gallons of skim per day, 24/7/365!"... well have you considered going up to the next size so that at some point your skimmer will not be producing skimmate? another way of doing that is when you add a refugium and your skimmer suddenly stops skimming youve reached that point. like i said, IMO a reasonable endpoint of a skimmer is when it sucks out so much crap that it stops skimming, then you can feed more, then the fishes and coral are fatter and get fewer diseases.
I just posted an old link to an experiment that determined what youre pulling out in skimmate. is it good to loose all those inorganics, including bicarb and salts that youre paying good money in the form of reef salt mixes? if a skimmer is a filter then it should take out bad and leave good- but does it do that well? or do most people just throw a lot of money into a skimmer because its less exhausting and impart more stability than water changes? How about a mature refugium? these take years of reefing to understand and lots of effort, you cant buy a red/white/european fuge off the shelf.
and if you mean oxygenating the reef, there are better ways such as an ozone reactor supplied by pressurized industrial grade oxygen. 1atmosphere of air is only 21% O2, which has an oxygen partial pressure of only 6x that dissolved in seawater, when you hit it with ozone and pressureized 90% O2 the dissolved oxygen and ORP are really high. but refilling an oxygen tank along with a CO2 is a pain in the neck. There were even air injection devices like what spinner used to make. but alas, these are also a PITA and that is why a skimmer is a good compromise for most reefers.