Hereof, can you get stronger without getting bigger?
The best way to get stronger but not bigger is to lift very heavy weights for very few repetitions. Training for muscle mass (hypertrophy) is all related to how many repetitions you do. If you do 6–12 repetitions with a moderately heavy weight, then your muscles will grow bigger.
One may also ask, do you have to build muscle to get stronger? The ONLY way to build muscle MASS with STRENGTH is that you MUST apply the 3 mechanisms to MUSCLE growth. Miss just one of them, and you WON'T grow or get STRONGER. Most people will tell you that you should chase just one goal at a time, but it is achievable to gain muscle mass while increasing strength.
Also question is, do you have to gain weight to gain strength?
While theoretically, you can put on muscle in a calorie surplus, even without lifting weights, adding some muscle building workouts to your plan is going to a be a huge factor in how much lean mass you can build. Heavier weight means increased strength and more strength means more muscle building potential.
Will I gain weight when building muscle?
Muscle is more dense than fat, but it takes up less space. That means if you gain muscle, your scale weight may go up even as you're slimming down. It's normal for you to lose inches, even if you're not losing weight. You can do with a home body fat scale, or by a trainer at your gym.