This sounds like a lens bias issue, especially since you say it gets worse the higher the f-stop. Many years ago, one of the lenses I had for my first SLR was like this. It shot fine up to f5.6 but if I stepped it down further than that, it would start to have issues until I learned to adjust the EV settings. Of course back then I'd shoot a roll over the weekend, turn it in for processing on Monday and get it back on Friday. My how things have changed...
My experience with that re-branded Pentax SLR and lens is what has me thinking the most likely cause of your trouble is an imperfect calibration between the Nikon and Sigma standards that is just ever so slightly off in the translation at the lens baseline of f2.8 and grows more and distinct as the f/stop increases.
You have stated that you always shoot in RAW. RAW is good for a number of things, but one of things it is known for is the ability to 'fix' exposure in post-production. Have you been able to fix this overexposure in post?
RAW is a format that is seemingly universal but in truth it is universally proprietary. Everyone decided on a name and no one decided to drop their in-house solution and pay someone else for the rights to use theirs. Each manufacturer produces the files in different ways. Nikon can adapt it for their lenses, but the Sigma lenses might not be perfectly matched up like Nikkor ones.
Next time your your setting up a shot with a high f/stop, try shooting in RAW+Fine JPG instead of just RAW. While your at it, after you've gotten the shots you want, try at least a few frames in full automatic. Compare the results before deciding the camera is faulty. Not saying that RAW is the problem or not, but why not see what it does for you in automatic. That will give an indication on if its in the lens or the camera.
I find that sometimes the little imp in my D3300 can beat my eyes, so I give him a chance occasionally to show me up. Mind you he doesn't do it often, and almost always when I'm shooting in conditions that are hard for my eyes to see with perfect clarity.
The Sigma 70-200 lenses like this one I found with a quick google search, seem to all have a slight dark bias, meaning they are engineered for lower-light photography. That's not a bad thing, it means that the lens has more depth in lower light shooting.
In fact letting more light in is the problem your talking about, and it might be just the way the optics in that particular lens work with the sensors in that particular camera body.
The reviews for the lens I linked to are really almost all positive, though a couple did mention some slight differences in performance from the equivalent Nikkor 70-200mm f2.8 AF lens.
While your Sigma 70-200mm is hardly a 'very-large-apature lens' this Wikipedia article explains an effect similar to what your dealing with, and may prove interesting reading.