This simple concept is basic to good tennis strokes: Your weight goes where your racquet goes.
Try these simple exercises and you'll see how that is true.
First, from the ready position try putting your non-dominant hand in the pocket on your dominant side. (Left hand in right pocket for righties or right hand in left pocket for lefties.) Repeat this from the ready position stance without pausing between changes in direction. The weight shift is automatic. Note the shoulder rotation as well.
Another simple exercise: take a closed forehand stance. Now extend both arms forward with your weight on your forward foot. Next extend both arms backwards, transferring your weight to the rearward foot. Now do it with your racquet in hand and repeat it several times. Got the picture? Add this to it: As you transfer your weight to your back leg, also rotate your body and bend your knees. Dennis Van Der Meer calls this "loading up" the back leg. You can feel the potential energy. You're ready!
These same concepts apply to the backhand strokes.
For your serve, try this: In your ready-to-serve stance, imagine looking toward the sideline at a large clock face. For right-handers, toward the net is nine o'clock; over your head is twelve o'clock, and rearward from the baseline is three o'clock. At your feet is six o'clock. (Of course, the 'nine' and 'three' are switched for left handers.)
With racquet in hand, extend it forward to nine o'clock, then down to six, then up and back to three. Again, this time shift your weight forward at nine; center it at six and onto the back foot at three o'clock.
Let's go a step further. Weight forward at nine o'clock, neutral at six, rearward at three. Hold that and let the racquet drop naturally toward your shoulder. Okay, now raise your racquet to twelve o'clock with your weight also rising to the occasion. Continue on to nine o'clock with a forward weight shift. Repeat this several times. Now speed it up a little with no pause in your motion. Both feet stay on the ground, but as you speed up you can drag your rearward toe forward toward nine o'clock. Apply this weight shift to your service motion and notice the improvement. You can "load up" here as well. Try it.
For the volley, it's a natural. In the volley, one of the things you must do is stomp your forward foot at contact. It's just another way of saying your weight goes where the racquet goes.
So diet if you must, but move the rest of your weight to where your racquet is going and feel the power added to your strokes.