At a simple intuitive level I would expect the weather to be more extreme. Here is my 'back of then envelope' take on it.
We have more energy in the climate system now than we did, say 50 years ago. We know this from 2 simple measures; atmospheric temperature, but more significantly, total ocean heat content.
The Earth is kept at its odd temperature by warming due to greenhouse gasses, countered by heat loss through the poles. It is a huge 'tropics to poles' heat engine.
If there is more energy in the whole system, then the heat transfers, oceanic and atmospheric should speed up and become more turbulent. This should increase weather variability.
Edit OM. "However, I am framing this around the energy change in the last ten years". Sure, but even though the atmospheric temp has levelled, the total Ocean Heat Content is still rising.
Here's another thought about extreme weather for you. Which of these two,cases has greater heat loss?
- earth with evenly distributed heat at 15deg,
- earth with half at 13deg and the other half at 17deg
The latter, because radiation is at the fourth power of temperature. The more unevenly heat is distributed across the earth, the greater is the heat loss through radiation.
Another point to make about extreme weather events is that they release huge energy to space. Big storms are made of a lot of cloud... and that's a lot of heat transported from the ocean (by evaporation) to the cloud body (latent heat released by condensation). Cloud both reduces heat gain to the earth, by reflection, and transports heat to space... radiated out of the cloud top. The bigger the storm, the more the earth is cooled.
Essentially, the climate moves to moderate the effect of any imposed change.