I don't know that all hurricanes expand in size as they weaken, but it is extremely common. The eventual outcome is simple enough to explain: it's a transfer of kinetic energy across a greater surface area allowing the energy to be dissipated over a broader area. One common reason for a hurricane to expand in size as it weakens is an EWRC. The process behind that is probably a little too complex to get into in this thread. Edit: I see Kory has covered a number of detailed reasons for why a hurricane's size might increase as it weakens.
But to answer your question, the shortest answer is that it all has to do with physics. You have latent heat in the ocean's water, and that is a form of energy just laying around ready to be used. A hurricane readily uses that heat energy and transfers it into its own system. That heat energy fuels the hurricane. A hurricane is basically a giant heat transfer machine. Just remember that the energy has to "go somewhere" (be dissipated) as the hurricane weakens. Mass and energy have an equivalence. Remember Einstein's famous E=mc^2 equation?
Broadly speaking, a hurricane can dissipate the energy it has in a number of ways. A larger storm and a smaller storm can be directly compared. Imagine a very small yet very intense hurricane. It may have a similar amount of energy to a much larger hurricane that only has winds of 85mph.
This is a rather complicated topic, so I'm simply trying to provide a very crude explanation to try to answer your question.
Here's a scientific paper that discusses some of the ways energy is transferred (or transformed) in a hurricane, what that means, what it does, etc.
We're actually still learning a ton about hurricanes. There is still plenty that we don't know. One of the reasons why we know hear a lot more about a hurricane's energy is because our understanding of the physics behind hurricanes has continued to mature. That, and Hurricane Ike really surprised a number of people, and that led to a deeper exploration of how to measure the amount of energy in a storm, the ways that energy might be transferred during the hurricane's lifecycle, and how that impacts we humans and our property and land.