Permanent night shift work is associated with adverse health effects, including elevated blood pressure (BP) and hypertension. Here, we examined the BP response to one night of forced wakefulness in a sitting position in a cohort without night shift work experience. According to a counterbalanced crossover design, 47 young adults with either obesity (N = 22; 10 women) or normal weight (N = 25; 11 women) participated in one night of sleep and one night of forced wakefulness under in-laboratory conditions. Resting ankle and brachial arterial BP were assessed in the morning, i.e., the time of the day when adverse cardiovascular events peak. After forced wakefulness, diastolic and mean arterial BP were ~4 mmHg higher at the ankle site and ~3 mmHg higher at the brachial site than after regular sleep (p < 0.05). The increase in BP following overnight forced wakefulness was more pronounced among men vs. women and more significant for diastolic BP at both sites among participants with normal weight vs. those with obesity. If confirmed in larger cohorts, including 24 h BP monitoring, people with occupations involving night shifts might benefit from regular BP monitoring. Particular attention should be paid to possible sex- and weight-specific effects of night shift work on BP.