Does leakage reactance of transformer depend on quantum of load?
I want to find whether the leakage reactance is affected by change in
  load on the secondary


Leakage reactance is due to the physical make up of the transformer i.e. the inability of the magnetic field of the primary to 100% couple with all windings of the secondary. As such it is fixed for a given transformer design and frequency.

However, the effect it might have on output regulation is very dependent on the load current because leakage reactance is a series impedance and the more current you take the more the volt drop is across it: -



Regards core losses (and in particular the possibility of core saturation causing a lowering of leakage inductance) I will say this: a transformer core will no more saturate on full secondary load than it does on no-load. This is because saturation is a function of \$B_m\$ (in the diagram above) and it is largely unaffected by secondary load currents. In other words, secondary load ampere turns produce equal and opposite ampere turns on the primary i.e. they cancel.