How tall do you have to be to ride a motorcycle with a 600cc engine?
It depends on experience people as short as 5.5" can handle a bike pretty well as compared to someone that's 6.2" it could get a little painful to keep you legs up. You don't have to be able to place both feet flat on the ground to ride a bike.
Sport bikes are not made for tall people but there are two bikes that are bigger than your 600cc and 1000cc bikes. One is the Suzuki 1300 Hayabusa and the other is the Kawasaki 1400 Ninja. I am 6'5 and have owned both but the Kawasaki fits me better and is superior to the Suzuki if it is 2012 or newer.