The governor is a rev limiter, if you are holding it at full throttle with no load you are likely engaging that limiter, a car will do the same thing if you floor it in neutral.
In other words, if your engine is "loping" at full throttle it is functioning properly, it keeps you from blowing it up.
A small engine shouldn't do that. It's a mechanical governor meant to maintain a constant rpm, whether the engine is loaded or not. That is its primary function. Secondary to that is to keep the engine from blowing up.
The rev limiter on a car engine is fundamentally different in its function, and is ONLY intended to keep the engine from blowing up.
On a small engine, as set up from the factory, setting the throttle or pushing the gas pedal in the case of a go kart is basically telling the engine how fast you want it to turn. It adjusts the throttle accordingly. When it hits the designated speed, the governor closes off the throttle. If you drive up a hill without moving the pedal, it will give you more throttle to maintain that speed, and so on.
In a car, pedal position dictates throttle position directly.
That's why you can put the pedal halfway down and you'll eventually end up going 70mph. If you go up a hill, you slow down unless YOU apply more throttle.
Small engine governors are more of a mechanical cruise control, that does also limit the top speed. But it SHOULD be able to hold a steady 3600 rpm with or without a load on it. "Looping" is generally referred to as "hunting" or "surging" and is usually indicative of another issue.
Too much oil in the case could conceivably interfere with the function of the flyweights in the governor, but these engines are often filled right to the threads. If there is a crosshatch section on the dipstick, try draining some oil until it's at the top of the marks. Usually these engines are designed so you can't overfill them as long as they're sitting flat though, and the dipstick only indicates a dangerously low condition.