There is some magnetising current needed to make the magnetic field oscillate at the mains frequency.
This current is fairly independent of the load current, and is a small fraction of the load current at large loads. However at small loads it can be a large proportion of the current. At no load, all the current taken by the primary is the magnetising current.
There are resistive losses in the windings. If you take those into account, the secondary voltage is:-
(v1 - I1*R1) * N - I2*R2
where R1 is the priamary resistance
R2 is the secondary resistance
N is the turns ratio.
As you increase the load, I2 and I1 increase, both of which reduce the secondary voltage from the ideal.