If the elevator is going at a constant speed, its acceleration is zero & hence the net force acting on it must be zero! So the upward force just balances the downward force.
Remember, the net force is the vector sum of all the forces acting. If they are equal & opposite, they add to zero.
If that bugs you, it may be because you don't think of gravity as another force that's acting on the object. It seems like the object is pulling back on the cables somehow.
If you shut off gravity & got the elevator going, no force would be required to keep it moving. With gravity, a force is needed to balance the downward gravitational force if the velocity is to be maintained. More on this later.