Text-to-image generators (T2Is) are liable to produce images that perpetuate social stereotypes, especially in regards to race or skin tone. We use a comprehensive set of 93 stigmatized identities to determine that three versions of Stable Diffusion (v1.5, v2.1, and XL) systematically associate stigmatized identities with certain skin tones in generated images. We find that SD XL produces skin tones that are 13.53% darker and 23.76% less red (both of which indicate higher likelihood of societal discrimination) than previous models and perpetuate societal stereotypes associating people of color with stigmatized identities. SD XL also shows approximately 30% less variability in skin tones when compared to previous models and 18.89-56.06% compared to human face datasets. Measuring variability through metrics which directly correspond to human perception suggest a similar pattern, where SD XL shows the least amount of variability in skin tones of people with stigmatized identities and depicts most (60.29%) stigmatized identities as being less diverse than non-stigmatized identities. Finally, SD shows more homogenization of skin tones of racial and ethnic identities compared to other stigmatized or non-stigmatized identities, reinforcing incorrect equivalence of biologically-determined skin tone and socially-constructed racial and ethnic identity. Because SD XL is the largest and most complex model and users prefer its generations compared to other models examined in this study, these findings have implications for the dynamics of bias amplification in T2Is, increasing representational harms and challenges generating diverse images depicting people with stigmatized identities.