Cricket bats are made in a variety of sizes and weights. If you want a lighter bat, there's no need to buy a new one; you can make your own bat lighter.
Brace the cricket bat firmly in position with your knee or with a clamp.
Use the plane to remove mass from the back of the cricket bat, trimming wood in strokes along the length of the bat.
Make sure that you remove equal amounts from both sides (left and right) as you trim the bat to maintain the balance of the heft.
Adjust the trim of the plane to affect the finished weighting and balance. If you remove more weight from the top of the bat, the bat will be harder to swing but you can deliver more power. If you remove more weight from the bottom, the bat will be easier to swing, but you will swing with less force.
Sand the bat with the sandpaper when you are satisfied with new weight of the bat to give it a smooth finish and avoid splintering.
Be conservative with the amount you trim. Remember, you can always take more weight off but putting weight back on is not so simple.