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I understand.
Your question is; "Why do star images grow?" (with longer exposures).
The answer is; because more energy is distributed according to their diffraction pattern/PSF/Airy Disk.
The wording in the Wikipedia article makes it sound like the Airy Disk is just a finite fuzzy blob around the location of a star. This is not the case (it is a simplification) and it is important to be aware of this in order to answer your question on why stars seem to 'grow'.
For purposes of Gaussian Curve fitting, the fuzzy blob gets pretty close to a Gaussian curve and we can leave it at that. And that's why Full Width Half Maximum measurements can be performed reliably and can be compare amongst eachother. Overexpose the fuzzy blob though and your Gaussian curve's top will be chopped off and/or distorted. This makes it harder to fit a Gaussian curve to and get FWHM results that you can compare with other measurements within the same image.
Now back to your question, "Why do star images grow?" (with longer exposures). You seem confused that stars can grow beyond the central fuzzy blob in the Airy Disk. The reason they can, is because the central fuzzy blob is not the end of the Airy Disk. The Airy disk has no end. Its pattern stretches out far beyond where the CCD sits.
Give the Airy Disk a bright enough star whose light needs spreading and it will saturate more and more CCD wells, further and further away from the central blob. The brighter the star, the further away from the center CCD wells get saturated. True, the central blob will be the first to completely saturate, but it doesn't stop there.
83% of all starlight falls in that central blob. But what if you got so much starlight that that 83% blob gets saturated? The other 17% all of a sudden becomes very important - that's where things start to saturate instead - the star starts to grow beyond the blob. It will take a lot of light to make it grow further and further (growing it just a single pixel will require more and more light) but it can definitely be done with enough photons. And because the spread function covers the whole CCD (and beyond), in theory, a single star can grow across the whole CCD, given enough photons.
I attached a visualisation of the underlying diffraction pattern that belongs to the tiny lonely 1-pixel star from the TIFF file I posted earlier. Diffraction is quite beautiful hey?
Stretch that TIFF far enough in PhotoShop and you'll see that tiny star grow according to this pattern. Try it; the data is really in there.
Note that non-linear stretching the TIFF is not what nature does. Nature just piles one more and more photons. You can do the same by adjusting the whitepoint in Photoshop, allowing pixels to gradually saturate. This is how a photograph gets exposed and how a star grows; the answer to your question.