If you have the kit lens that came with the 60D then this is a property of the lens, not the camera. Your camera is fine and functioning normally.
I’m guessing that your lens is 18-135mm f/3.5-5.6. That means that at 18mm (very wide) your aperture will be at 3.5. As you zoom in towards 135mm your aperture will close up. If you reach 135mm your aperture will be 5.6. In the simplest terms it’s very costly to build a lens that stays at a given aperture as you zoom in because it’s hard to transmit light as efficiently as you zoom. So typically concessions are made to keep the cost of the lens down. Now if you want a lens that stays at f/2.8 throughout the zoom range then you’re going to pay for it (cf – https://www.amazon.com/Canon-70-200mm-2-8L-Telephoto-Cameras/dp/B0033PRWSW/ ).
From Wikipedia:
Zoom lenses typically have a maximum relative aperture (minimum f-number) of f/2.8 to f/6.3 through their range. High-end lenses will have a constant aperture, such as f/2.8 or f/4, which means that the relative aperture will stay the same throughout the zoom range. A more typical consumer zoom will have a variable maximum relative aperture, since it is harder and more expensive to keep the maximum relative aperture proportional to focal length at long focal lengths; f/3.5 to f/5.6 is an example of a common variable aperture range in a consumer zoom lens.
Here’s some additional info for you to read up on:
https://www.bhphotovideo.com/indepth/photography/tips-solutions/variable-apertures-and-depth-field
https://en.wikipedia.org/wiki/Aperture
https://en.wikipedia.org/wiki/Lens_speed
Ryan Holmes
http://www.ryanholmes.me
@CutColorPost