Previous studies of survey data for the United States and other countries find that on average women tend to understate their body weight, while on average both men and women overstate their height. Social norms have been posited as a potential explanation for misreporting of weight and height, but researchers disagree on the validity of that explanation. This paper is the first to present a theoretical model of self-reporting behavior for weight and height that explicitly incorporates social desirability bias. The model generates testable implications that can be contrasted with predictions based on alternative explanations for self-reporting errors. Using data from the National Health and Nutrition Examination Survey (NHANES) from 1990-2010, we find that self-reporting patterns for both weight and body mass index (BMI) offer robust evidence of social desirability bias, such that reports are biased (from both sides) towards social norms. The BMI norm inferred for women lies squarely within the range considered "healthy" by public health officials, while the BMI norm inferred for men lies just above this healthy range. Lack of awareness of one's current body weight may explain the presence of large (negative) self-reporting errors among those with very high values of examined weight, but the evidence of social desirability bias is robust to this alternative explanation over most of the weight distribution. Social desirability bias in self-reporting of height is observed primarily among those of below-average height and no clear height norms are discernible. The framework also helps to explain previous findings that the degree of self-reporting bias in weight depends on the survey mode.