Is the Sun getting bigger?
Short answer: Yes.
Long answer: In the Sun, there is a rough balance between the outward pressure created by the Sun's nuclear fusion and the inward force of gravity holding it all together. This balance is good enough to keep the Sun in its current state for billions of years, but it's not perfect and there is a very small imbalance. As the Sun uses up its fuel by fusing hydrogen into helium, its core is slowly collapsing and heating up while the outer layers are growing larger.
Oddly, the Sun is actually getting less massive as it gets bigger. This is part of the imbalance—as the mass decreases, so does the gravitational force holding the Sun together, allowing the outward pressure to "win" and increase the Sun's diameter.
The Sun has increased in size by around 20% since its formation around 4.5 billion years ago. It will continue slowly increasing in size until about 5 or 6 billion years in the future, when it will start changing much faster. At this point it will turn into a red giant, rapidly increasing in size until its diameter is about equal to the orbit of Venus or even Earth.
We can't directly measure the change in size yet—our prediction is based on our understanding of astrophysics and observations of solar wind, etc. Over the next few hundred years it's likely that we'll develop technology sensitive enough to measure the change in size directly.
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Author: Dave Owen