Yes, a skid steer's center of gravity changes when there is something in the bucket. Most of a skid steer's weight is located in the rear of the machine, between the wheels. The center of gravity for a skid steer changes on the basis of the location of the attachment, the weight of the attachment, and any additional weight added to the attachment. When there is weight in the front of the skid steer, either in a bucket or on an attachment (as with a pallet fork), the skid steer's center of gravity shifts forward and upward. When transporting a load in the front bucket or with an attachment, carry the load low to the ground to maintain a low center of gravity.
For more information about skid steers, click here to access the article "Skid Steer Safety."