Just found this.. might answer both of our questions.
When a skimmer is larger and the system is a low nutrient system, then there might not be enough organics for the skimmer to maintain a head to export the skimmate. It is kinda like building a large car engine and using an undersized fuel pump... so the engine is just starved. A lot of times, folks will buy a big skimmer and it will do well for a few months. After a while, the skimmate production drops... In reality, the skimmer caught up to the tank's organics and then settled down to a more normal output. But, some folks will see this as their current skimmer "wearing down" and go out and buy the next size up. As a result, this skimmer does "ok" for a while the completely drops off to near nothing. That is over skimming.
Large skimmers, because of their large neck size requires more organics to build the head than smaller neck skimmers. However, large skimmer necks handle more air then smaller ones so they can skim more when there is enough organics.
I am one of those who is over skimming. I have to have a large bioload and carbon dose for my skimmer to produce anything. Still, because carbon can excite a skimmer, oversizing the skimmer is a good idea and it maintains the O2 level better.