A smaller aperture is actually a smaller f-number.
F/16 is a much smaller number than f/2 is, because they are fractions.
The f-number describes the size of the lens aperture as a function of the lens focal length. In other words, the letter f is a variable that is the lens focal length.
A 100 mm lens set to f/4 has a lens aperture has a 25 mm diameter - 100/4 = 25. A 100 mm lens set to f/8 has a lens aperture that has only 12.5 mm diameter - 100/8 = 12.5
A 200 mm lens also set to f/4 has a lens aperture that has a 50 mm diameter - 200/4 = 50. A 200 mm lens set to f/8 has a lens aperture that has a 25 mm diameter - 200/8 = 25
So you can see that a 200 mm lens set to f/8 has the same lens aperture diameter as a 100 mm lens that is set to f/4 - 25 mm.
Basically, a lens aperture of 25 mm lets in the same amount of light regardless the lens focal length.
You may want to note however - A 'stop' of lens aperture doubles, or halves, the amount of light entering through the lens aperture. The amount of light a lens aperture can let in is dependent on the aperture's area, not it's diameter.
Your camera is likely set to the factory default of adjusting lens aperture in 1/3 stop steps.
The full stop steps are f/1 - f/1.4 - f/2 - f/2.8 - f/4 - f/5.6 - f/8 - f/11 - f/16 - f/22 - f/32 - etc.
In other words, if lens focal length is not changed f/5.6 lets in twice as much light as f/8 does, or f/8 lets in 1/2 as much light as f/5.6 does.