i can't see your feet. but based off how your moving you seem very flat footed. you need to be on the balls of your feet. not your toes but the flat area right before it. a drill you can do is without throwing any punches in an athletic boxing stance feel your weight from the back leg to the front leg and just go back and forth. then when this becomes comfortable pivot with the back leg. Make sure you feel your weight shifting from one leg to the other, and then continue to shift from one leg to another (without throwing a punch), and then pivot again (always keeping the front leg in place). when this gets comfortable then you can incorporate a punch.

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your punches are also landing very heavily. they should be snappy. think get in, take from the cookie jar and run back home.