Stills zooms almost routinely ramp max aperture at one end of their focal range. Yours is ramping down to f/4 at it’s most narrow focal length which sounds about right. Do a test: stop down to f/4 and see if the ramping still occurs or if the lens commits to that stop throughout its entire focal range. If it does, then f/4 is that lenses’ sweet spot, so only stop up to f/2.8 when needed.
Stills lenses just aren’t made to be as precise as cine ones. They don’t need to be. Cine lenses, however, have a much tougher job so their standards are higher. Of course your Sigma cine zoom performs better than a stills lens. Stills lenses look great for every one photo they take. Cine lenses have to look good at 24 frames per second for hours.
On my stills lenses, when I don’t want ramping (like, for video), I find the maximum formula-stop where ramping does not occur across the zoom range, and lock my exposure there. This ramping occurs even in Canon L lenses.
Stills lenses are not suitable for cinema production for this reason, and many others. All stills lenses ramp their f-stops (sometimes imperceptably, sometimes obviously), and they also breathe when racking focus, and have more obvious aberrations than do cinema lenses. Zoom lenses of either class always have worse optics than primes because they are so complicated and have many optical and mechanical elements.
Proper cinema lenses do not exhibit the same flaws as obviously as stills lenses. The very nice cinema lenses have very subtle aberations that usually don’t present unless you’re aiming at a test chart.