The Power you generate with a punch or kick is equal to your size multiplied by the speed of your technique. Your size in this case is equal to your Mass which is your weight divided by gravity, so the more you weigh the harder you can hit. The Mass of your arm or leg is not as great as the Mass of your Body. In order to increase the Mass behind your attack a martial arts uses body mechanics to link your whole body together, thereby increasing the Mass behind each technique. Without this proper technique to link your body movements, each component will act independently with only its own component Mass. The Mass of my limb might be equal to 5 percent of the Mass of my whole body.
The amount of weight you can move in the gym has no direct impact on your ability to hit hard. Lifting weights equals Work which would be applicable to pushing someone or overpowering someone, but not to striking someone. Lifting weights can increase you Mass which would increase you're Power. The only other way for a full grown adult to increase their Mass would be through Fat. Other than the obvious heath risks associated with increased Fat, Muscle has a Mass 10 time greater than an equal amount of Fat.
Speed is equal to the distance you can move divided by the time it takes you to get there. Speed can be increased through practicing the movements at speed with repetition. Certain dynamic exercises such as clap push ups, and Olympic lifting exercises can increase both Muscle mass and speed at the same time. Any exercise done correctly and safely that combines resistance and explosive movements will increase your speed. Another important physical characteristic for increased speed is staying relaxed. If you tense your muscle during a strike it is like pressing the brake and accelerator at the same time, it will only slow you down.
Relaxing also has additional benefits. A relaxed body will help your mind stay calm and allow for a clear thought. In stressful situations, like competition or a real life self defense situation, your body naturally wants to tense up for protection. This tension adds to stress and feeds into your bodies fight or flight program. Stressed fighters often get stuck in a mental state that does not allow them the mental agility necessary for good decision making. Fighters often get stuck in action loops, repeating the same technique over and over again regardless of its outcome, because they are no longer capable of rational thought. A second Benefit of relaxation is that it allows you to "roll with a punch" allowing you to reduce the impact of a blow by going with its force. The alternative is to tense the body trying to use your muscle as armor against blows. With tension you will take the full force of the blow and can only hope that you don't get hurt.