Tornadoes have been known to move all sorts of heavy objects, tipping over trains and sucking up cows, so the weight of a shark isn't likely to pose a huge barrier in our sharknado scenario. Great white sharks can weigh up to 5,000 pounds (2,268 kilograms) and sometimes even more [source: National Geographic]. The average weight of a mature dairy cow is about 1,400 pounds (635 kilograms) [source: Purdue University]. If a tornado can pick up a few cows, it definitely should be able to support the weight of a great white, as long as you have the right amount of wind.
To figure out the wind speed the waterspout must have to pick up a great white, we need to know the terminal velocity of a shark (the speed the shark would fall if you pushed it out of an airplane). Since people don't normally throw sharks out of planes, not all the parameters of the equation for terminal velocity are worked out specifically for sharks. To do the calculation, we're going to have to make some assumptions about the drag of a shark and its surface area, but we can still come up with a ballpark figure.
To fill our equation in with numbers, we'll use 2,268 kilograms for the great white's weight, known constants for acceleration due to gravity (9.8 meters per second squared) and air density (1.2 kilograms per cubic meter), an assumed drag coefficient of 1 (unitless value) and an assumed surface area of 4.6 square meters based on the average length for this sea predator (4.6 meters, or 15 feet) [source: National Geographic].
Crunching those numbers through our calculator gives us the terminal velocity for a great white shark.
Terminal velocity = 89.7 m/s
Translating that into the wind speed we'd need to lift the shark off the ground, we get about 200 mph (322 kph). Waterspouts generally have speeds of less than 100 mph (161 kph), so this would have to be one massively strong weather system. It would have to rate at least a 3 or 4 on the Fujita Tornado Damage Scale (severe to devastating damage where trains can be overturned, cars thrown and houses leveled) [sources: Kellogg, Storm Prediction Center].