Try this: from your boxing stance put all of your wt onto your left leg and lean directly over that (straight) leg. Then turn your hips to the left until the right hip approximates the center line of the body; this is best accomplished by pivoting sharply inwrd on the toe (the ball) of the right foot. The turn of the hip in turn will twist the shoulder, and that would drive out the right fist. The wt is not shifted ffrom a push and the right foot does not push at all- it just twists.
Then try it the other way- get in your stance and put your wweight unto the rt leg; the right heel should be off the floor at start, so you set it flat toe pointed to the side leg straight. The left heel is now off the floor and you pivot sharply on the left toe again inward and this turn thwe hip and shoulder through to center. The key to getting wt into your punch- getting concussive force and not pushing force- is in creating an anchor point or hinged side of thwe body (the side with the straight leg) and then slamming the other side through the center line, like slamming a door. It isn't a push- though many fighters do push their right hnds- but more of a screwing in motion.