Two set of studies were conducted to better understand grades and grading practices in physics courses, and how these might influence demographic representational disparities in physics. The first study investigates the relationships between grades and the student-level factors of standardized test scores, (binary) gender, underrepresented minority (URM) status, first generation (FG) status, citizenship status, and age of over 20 000 students enrolled in algebra-based and calculus-based introductory physics courses. Consistent with other studies, we find differences in mean grades for all of these factors, except for gender, and when standardized test scores are included in a regression model predicting grades, the demographic differences in grades decreases, though typically remain nonzero. We also find gender by test score and URM by test score interactions when predicting grades. The second study examines grade component scores, and replicates the finding that compared to men, women achieve higher scores on nonexam components and lower scores on exam components. We also find that the gap in score between URM and FG students and their counterparts is less for non-exam components than for exam components. Because of these differentials in components, we compared different models of grade components weighting and find that women and URM students differentially benefit from stronger weighting of nonexam components. While the benefit to grades is relatively small, the relative shift in percentages of grade rates of A, D, and F can have dramatic differential shifts. We also find that while exam components are moderately strongly correlated with standardized tests scores, nonexam components are not. These results suggest that grade component weighting is inevitably tied to issues of demographic equity, in the sense that altering the weights may change demographic disparities in grades and change the dependency of grades on standardized test scores. We conclude with a call for more attention to grading practices and what is rewarded in introductory physics courses.