Your issue (your problem) is not so much one of white balance, but one of exposure. White looks white when it is given more exposure than a camera's reflected light metering system tends to indicate. The camera's built-in exposure meter will tend to make a white paper look gray. Adding exposure, by slowing down the shutter, will "lift" the exposure for the paper, and make it look white. If the shutter time is sped up, the paper will be rendered darker and darker, first as slightly dark gray, then darker gray, and so on. Now...this is the thing...with MANY small light boxes and setups that have the lights placed fairly close to the shooting area, the light is not very even in its intensity, as measured by a photographic light meter. The light produced by a small lightbox type of setup will appear, to the human eye, to be quite even in intensity. Human vision is incredibly adept at adapting to differences, and we see things differently than does a camera.
As I see your problem, your gray issue is one of un-even lighting, and un-even,different degrees of camera exposure value. In close-range lighting, there is a well-known issue that arises from the Inverse Square Law. The ISL is what you're running into here. Because the lighting is coming from bulbs that are physically CLOSE TO the subjects, the rate of fall-off in light intensity is VERY rapid, even across distances as short as a few inches, and THAT is why (according to basic science,not personal opinion) your background paper is going from white, to light gray; your first teacup shot shows this effect VERY obviously, and is a classic example of the problems associated with lighting small products with simple lighting that is placed too CLOSE, physically, to the subject.
If you want more-even, and more-white lighting, you need to 1) increase the distance of the lights from the subject. Increasing the distance of the light source will lead, directly, to light that is more-even across distances. Again...this is a very well-known issue, and it's a drawback that the makers of small light boxes are not going to emphasize. A quick and fast lighting set-up, like a light box, or one softbox just plopped down close to the shooting table, will often lead to un-even illumination that the human eye will accommodate for, but which the camera,and the light meter, can and will "see" as un-even.
When dealing with white paper: even a slight degree of under-exposure, or under-lighting, will very rapidly, introduce a gray tinge to the image. Look to your early image, the one of the beautiful teacup:
proxy.php the white-white areas have the most light. The areas that are less-white? Those are/were receiving LESS light, and are being rendered AS-EXPECTED, by science.
There are solutions to the problem...and the solution is NOT a white balance correction. The solution is different lighting strategy!
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