The 1/8 to 1/30 range your smaller-aperture shots are made at is kind of a dangerous zone for mirror slap and shutter vibration. On many lighter-weight camera bodies and lighter-duty tripod heads, there can,at times, be some vibration patterns that make exposures in the 1/8 to 1/30 second range prone to softness from the slap of the mirror going up, then the first shutter curtain racing across the film plane and exposing the film/sensor, and then the second shutter curtain closing to end the exposure.
On a danger zone shutter speed, like say 1/8 second, the mirror creates slap as it swings up...then the first curtain thunks open...and so there are two (potential) vibration-causing effects, which are recorded in a brief exposure that takes as long to make as it takes for the vibrations to quell; longer exposures, like 4 to 6 seconds can actually appear sharper and less-affected by vibration than those in the 1/4 to 1/30 second range. One solution is to use a flash exposure to test sharpness...the flash duration is very,very brief, and guarantees there will not be sharpness lost due to camera vibration.
That faded wood test target is not the best target....I'd rather see a page ripped from a magazine taped to a wall or something like that. The test target looks best in the first shot. Focusing accuracy is huge on these kinds of tests. I see that the shot done at f/6.3 and 1/13 second looks very slightly less-sharp than the one done at f/8 and 1/8 second; that could be due to any number of factors--mirror slap, slight camera vibration, or a very minute focusing error, or a bit of focus shift on the lens; many lenses will shift their point of focus a bit between wide-open and the shooting aperture.
These kinds of tests demand really,really careful control if the tests are to be 100 percent trustworthy. Can you use your camera's Live View, to determine if there is some focus shift by focusing with the lens wide-open, and shooting a series of test shots at one specific aperture, and then doing another series of shots focusing with the lens stopped down to the shooting aperture? (Does your body even offer Live View?)