Answer:
If you use strength exercise to increase your muscle tissue, you will be heavier (all things being equal) because a given volume of muscle is heavier than that same volume of fat.
However, if you are using strength exercise correctly and eating correctly (healthy foods) as you train, you will simultaneously lose body fat. In other words, your body composition will significantly improve. By that, if you were to lose 10 or 20 pounds of fat while gaining 10 or 20 pounds of muscle, you would look far better, feel better, and be healthier even though your weight did not change
You will not gain more weight fat out weight muscle and muscle does not weight as much so keep strength exercise going.