Since vitamin d is fat-soluble, do you have to have much fat to store it in? Are very skinny people unable to store adequate vitamin d?

No. Actually, obese people are at higher risk of vitamin d deficiency than skinnier people. Obese people tend to have lower vitamin d levels for many reasons including the fact that they absorb vitamin d in their subcutaneous fat stores, making vitamin d less bioavailable. Obese people may be less able to convert vitamin d into its hormonally active form. Obese people may require more sun to make d.