Looking at the image, it seems the primary culprit is either camera movement/vibration or a slightly soft lens. The tree trunk is just as blurry as many of the other parts of the image, so the wind may be a factor with regard to the leaves and grass, but is it not the only factor with regard to the entire image.
At 1/15 second you are squarely in the middle of the shutter speed range that is most affected by mirror movement. A faster shutter time will be completed before the vibrations reach the parts that matter (sensor and lens). A longer shutter time allows for exposure to continue after the vibrations have ceased. A few controlled tests I have seen put the range for mirror movement induced blur from about 1/160 second down to about 1 second. The greatest effect is seen from between 1/80 second to about 1/3 second. 1/15 is exactly in between these. It is five times shorter than 1/3 second and five times longer than 1/80 second.
1/15 second is also too slow for anything outdoors that can move in the breeze. Anything faster than about 1/200 second should eliminate any blur due to vibrations from the mirror movement and would reduce the movements of the leaves due to wind by a factor of about 13.
F/11 is already just beyond the diffraction limited aperture (DLA) of f/10.1 for the EOS 5D Mark III. You won't see much of the effects of diffraction at f/11, even when pixel peeping, but you will see a little bit. Certain types of sharpening tend to exacerbate diffraction. Open up the aperture to f/8 or even f/5.6 and you should still have enough depth of field for what you are trying to do. This will also help with using a shorter shutter time without raising the ISO too much. ISO 400, F/5.6, and 1/200 second would be my starting point. With most Canon DSLRs, including the 5D Mark III, you probably want to avoid the '+1/3 stop' ISO settings (125, 250, 500, 1000, etc.).
Just because your camera is on a tripod does not mean it is motionless. Wind can and often does have an effect on tripod stability. A strap left attached to the camera can act like a sail when the wind is blowing, making the problem even worse. Allowing everything to 'settle down' after touching the camera or tripod can also take several seconds. The lighter the tripod, the longer it takes.
Although it is hard to say for certain due to effects of the apparent camera motion/vibration, it appears to me that the point of sharpest focus is a bit beyond the large tree.
Post processing also plays a part. Sometimes a little bit of something does better than a lot of the same thing. Oversaturation, even when limited to only a single color channel, can cause things that were properly focused to look blurry. Too much sharpening can also make slightly out of focus areas look even blurrier. Increasing 'local contrast' can do the same thing. The presence of a bit of 'halo effect' where one of the tree's branches is in front of a darker cloud indicates you may have pushed the 'clarity' slider a bit too far.
I have an EF 24-70mm f/2.8 L. It is a very good lens. It is not perfect. But most of the imperfections are most evident when the lens is used wide open. At f/8 or so I doubt you'll see much, if any, difference between a properly aligned original version of the lens and the EF 24-70mm f/2.8 L II.
The unique 'backwards zoom' design of the original Canon 24-70mm f/2.8 and where this places the optical adjustment points makes it highly sensitive to bumps and other minor impacts to the front of the lens barrel, especially when the front inner barrel is extended. Roger Cicala has written a few blog articles that discuss this particular lens. If you read them, though, please be sure to read them in their entirety and pay attention when he says things such as,
And before I go further, please raise your right hand and repeat after me: “I do solemnly swear not to be an obnoxious fanboy and quote this article out of context for Canon-bashing purposes.” Because trust me on this: Canon faired very, very well in our testing, with only this one lens being an outlier. Other brands definitely are not better. This one got to be the example simply because we started testing Canon lenses first, and because we have more copies of them.
I’m going to use a Canon 24-70mm f/2.8L lens as an example, mostly because it’s a lens we know well and partly because adjusting it is pretty straightforward and the adjustments are easy to photograph. Not all lenses are as easy to work on. The copy we’re using for this demonstration has a fairly typical story: it was dropped, causing the filter ring to bend.
Optically Adjusting a Lens
The Limits of Variation
One of the nice things about the design of this lens is that the hood is attached to the main barrel and protects the inner barrel from impacts. Since the lens is most extended at the shortest focal length and most retracted at the longest focal length the hood also provides good shielding from off axis light throughout the zoom range. Because of the way the hood protects the front group from impacts, I never take my 24-70 f/2.8 out into 'the wild' without the hood attached due to the way that even relatively minor impacts to the front barrel can knock the front group out of proper alignment.