Weightlifting helps but, it's not JUST weightlifting, it's how you lift weights. If you lift weights in the way that you do quick lifts, then it can help because you are training your fast twitch muscles to do quick snaps with a lot of resistance. The technique goes like this, you lift the weight, then lower it smoothly, hold for around one whole breath so the weight is not that heavy, then push as fast you can while still maintaining form.Repeat the process until you are tired. Keep increasing the weight every week. The power in a punch is how quick you can snap it while being stable, and maintaining strength against the resistance you are punching, not necessarily punching and pushing through. If you watch how mike tyson hit the punching bag, he did quick snaps with all his will. He also used his legs properly. The legs help you keep stable and make use of all that quick energy being released. If you have weak legs, your punches won't be that powerful because you will be moving every time you connect a punch, and that makes the punch not that effective. The same goes for your core muscles, and back muscles.
The other secret is diet. Hint carbohydrates!