In-Fisherman magazine has some tips this month on weighing fish:
The best method to weigh fish is when they are supported inside a net.
With a cradle net, use a rope with loops at each end to slide over the ends of two handles. Center the scale to get a weight, then subtract the weight of the rope and the wet net.
With a dip net, turn the hoop vertical to secure and brace the fish. Hook the scale on the side of the hoop, then subtract the weight of the wet net.
If you don't have a scale handy, a good method to approximate the weight utilizes a sewing tape to measure the fish. Use this formula: (Girth - 1/2 inch) x (girth - 1/2 inch) x length, divided by 800.
One way to measure girth is to attach a sewing tape measure to a 60-inch floating ruler. Attach the tape at about the 25-inch line on the 60-inch ruler. Keep the tape wrapped on the ruler, held in place with a rubber band. Remove the rubber band, unravel the tape, and after measuring fish length, wrap the tape around the fish, then slide the tape forward and back to find the fish's girth, which should be measured at the widest point.