Aperture is not measured or expressed in absolute numbers, the way shutter speed is. A shutter speed of 1/250 exposes the film or sensor for 1/250th of a second, whether you have a 50mm lens or a 300mm lens. Where aperture gets weird is that the physical size of the aperture does need to change depending on the focal length of the lens... A aperture of say, 5mm (pulling a random number out of my butt) allows a certain amount of light to contribute to an exposure through a 50mm lens, but that physical-size aperture allows far less light to contribute to an exposure through a 300mm lens. The correct aperture is proportional to the lens's focal length, and that's where the f numbers come from. It works out that an aperture opening that is 1/8 the lens's focal length contributes the exact same amount of light to an exposure whether the lens if 50mm or 500mm. A physical aperture of 6.25mm in a 50mm lens (50/8) produces the same light gathering as a physical aperture size of 62.5mm in a 500mm lens (500/8.) We express that aperture value as f:8. We don't care what the physical size of the aperture opening is, but because of the way the optical properties of lenses works, The exposure value of f:8 is the same, regardless of focal length.
That's actually one reason you don't see very long lenses with very large apertures... The lens barrel of a common 70-300mm zoom lens simply isn't large enough to have an iris that can open to 75mm, which would be f:4. There are long lenses with large apertures out there, like a 600mm f:4, but they are expensive. By the way, when a lens is capable of larger apertures, we call it a fast lens; a large aperture lets in enough light to allow for faster shutter speeds.
Your question about changing the aperture with zoom has merit, but not the way you're thinking of it. You can't separate light from image. The aperture is not a "shade" in front of the lens, it's an iris between certain elements of the lens. A large iris lets in more light, resulting in more exposure, and a small iris lets in less light, resulting in less exposure. If we had to set aperture size by its physical dimension, we'd have to carry around a book of tables to match desired exposure settings to focal length, and photography would be far less fun than it is. the fact that the aperture behaves proportionally to focal length saves us that headache, and lets us express aperture as the simple fraction of the focal length. Remember, an aperture 1/8 (or 1/4, or 1/16) the size of the lens's focal length allows the same exposure of light through the lens, no matter the focal length, so we simply say f:8 (or f:4 or f:16.) That's also why large apertures have small numbers. An aperture of f:1.4 is a common maximum aperture for lenses in the 50mm range. A 500mm lens couldn't economically be built large enough to carry an iris capable of f:1.4! If you want an example of a cost-no-object fast, long lens, Google the Sigma 200-500 f:2.8 lens, yours for about $26,000!
Finally, an explanation of why f-numbers for apertures aren't sequential. Exposure stops are discussed as doubling or halving the exposure; a 1-stop difference is half the exposure or double the exposure, with "exposure" being the amount of light collected by the film or sensor. Shutter speeds is easy: double the shutter speed, say from 1/125 to 1/250, you get half of the exposure, i.e. a one-stop change. Aperture stops are f:1.4, f:2, f:2.8, f:4, f:5.6, f:8, f:11, f:16, etc. Now aperture work by the area of the iris opening, which involves a squaring factor. If I want to move 1 stop of aperture, I don't double or halve the f-number, I have to multiply or divide it by the square root of 2. Doubling or halving the f-number changes your exposure by 2 stops, not one. That's why the sequence of f-numbers on the lens seems... odd. 1-stop differences in f-stops are measured as 1.4 times the next one.
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