I am with superdave and Paul. If you have the 8.8 rear, which you probably do, the movement is normal. IF it really concerns you, you can have someone open the diff and see if the rubber-rings on the ends of the driveshaft are still intact. They kind of buffer the c-clip that holds the axles on the side-gears of the diff. The play is OK since the c-clips are captured and cannot come off the axles (thank-god) but the c-clip itself can take a beating if the play is excessive. 1/16" is not excessive.

Randy