Here are my settings. Aperture preferred. ISO 800. Set to fill flash. Camera on tripod. Steady shot off. At f14 shutter speed selected is 1/125 and image is too dark. The shutter speed doesn't change until f is down to about 5.6. At 5.6 image is a bit soft. I would prefer to shoot with smaller aperture because I get sharper images. Using Sigma 70-300 apo zoom at 300 setting. Thanks for any advice.
As you change the aperture, the speed should automatically change to keep the focus correct. With aperture at f14 and shutter speed at 1/125 (if the photo was well exposed and everything is working correctly) A change to f5.6 (a 3x increase in aperture size) the speed should increase to 1/1000 (which is a reduction in speed) to maintain that exposure. If that is not happening I would say that your iris diaphragm is sticking or that there is something wrong with the camera. Check to see if the diaphragm has mold or dirt on it. if not then the camera may have a faulty shutter (dirt again).
By the way, for your lens/camera combination, f14 at 1/125 (if an accurate exposure) you may be running into diffraction problems. With most lenses, the peak sharpness, or sweet spot is at ~ f8, as you go down to f22, diffraction will reduce the sharpness greatly. Conversely going up to f5.6 reduces depth of field but totally eliminates diffraction. You could have used f8 at 1/500 (the equivalent setting) and saved having to use the tripod,had good depth of field and possibly the ultimate sharpness for the lens used.
Sony A7, A850, A77, A700 || Sony>> 70-300G, 28-75 f2.8 SAM, 16-80CZ, 50 f1.4, FE 28-70 OSS, FE 24-70CZ f4 OSS, LA-EA4 || Minolta>> 300 f4 G HS, 200 f2.8 G HS, 100 f2.8 (D) Macro, 50 f1.7, 28 f2.8, 28-135 f4-4.5, 70-210 f4, 500 f8 Reflex, TC x 1.4 HS, TC x 2 HS. || Sigma 21-35 f3.5-4.2. || Tamron SP 24-135.