Now you've done made me place an order for 3-5 oz leather lol. One of the first things a pro leatherworker will when examing your is to check the edges.

Are you having a problem grooving or punching? If it's punching are you placing fingers on eqch side of where the awl goes through? If it's grooving you can use double sided tape or contact cement and glue the leather to some plexiglass or even your cutting board.