Should I watch my weight while trying to gain muscle mass?

Depends. It depends. Muscle mass for strength needs more body weight. For fitness or lean body mass does not. Muscle weighs more than fat so fat replaced by muscle may not lose weight. Typical daily activities require about 1500-2000 calories. Take most of your calories in protein. Add more calories only equal to amount of exercise. Measure excess fat by triceps skin fold. Leaner is healthier.