On top of the obvious diffraction effect, the other thing to consider is that each step in a narrower aperture will lower the light level, meaning you will need to compensate by either slowing the shutter speed or raising the ISO to get the same exposure/brightness.
That's all well and good excepting for two considerations: raising the ISO means that you are amplifying a low-light image, and in doing that you are amplifying noise, which can be detrimental to your image quality. This combined with diffraction could in fact be, well, not good when you are viewing at a fairly large image size.
Slowing the shutter will let more light in so that you don't need to increase the ISO, but the problem there is your shot will be vulnerable to any vibration of the camera/lens, which will show up as image blur. The vibration could come from any of several sources -- you pushing the shutter button, the mirror "slapping up" to take the picture, a car driving by, a breeze, an unsteady tripod, or a lens on a tripod but with the IS on, acting "funny".
So, again, add any vibration blur to the diffraction effect, and you will get worse additive results.
So, yeah, diffraction alone begins to show up as you stop down, noticeable when you view an image at 100%, less noticeable at a more "normal" view size. But like you observed, on a 7D you will start to notice it at f/11 or even wider if you are doing real technical analysis.
So, in this testing you take that into consideration, and then realize that it is up to you to do anything and everything possible to cut down on camera shake. I consider a sturdy tripod and a cable or wireless/remote release to be "basic equipment" and then knowing how to use things like mirror lockup and, in the absence of a cable/remote release the self-time are critical skills to have not just for this type of testing, but for field photography where optimal sharpness can make a difference, such as landscape and other scenic photography, these skills and the needed accessories are also critical.