(1) Background: To analyze the prevalence of physical activity (PA) according to the presence of overweight or obesity and other sociodemographic factors in the Spanish adult population. (2) Methods: Cross-sectional study using the European Health Interview Surveys for Spain from 2014 and 2020. (3) Results: In overweight and obese people, the percentage of those who reported not performing any type of PA remained constant between 2014 and 2020, while a statistically significant increase was observed in the percentage of people who walked for 10 min a day and exercised at least 2 days a week. The probability of being obese with respect to normal weight was higher in individuals who reported not engaging in PA during leisure time (OR 1.42; 95% CI 1.31–1.53), those who did not walk 10 min a day at least 2 days a week (OR 1.25; 95% CI 1.15–1.35), and those who did not exercise at least 2 days a week (OR 1.42; 95% CI 1.32–1.53). The probability of being overweight was higher in individuals who reported not performing PA during leisure time (OR 1.07; 95% CI 1.02–1.15) and in those who did not exercise at least 2 days per week (OR 1.15; 95% CI 1.09–1.22). (4) Conclusions: Small increases in PA have been observed in both overweight and obese individuals from 2014 to 2020.