Hello everyboby!
Core losses (mostly hysteresis and eddy currents [Foucault currents]) are not going to change (theoretically and with the usual simplifications) with the load increase. But load losses (I2R) will.
About the 6.5 KW you mention, Scott35 wrote an excellent answer (and previously Bjarney have said something about it) explaining that those are not KW. Some part or it, the lesser one, are KVA, and the other, the bigger one are KVAR (I’ll bet my shoes that the ratio is about 1 to 5).
So, when load is starting to be added to the transformer, the transformer imput impedance will start gain resistance and loose reactance. This means that the Q factor of the transformer equivalent circuit will start to decrease and the “stored energy” over “dissipated energy” ratio will go down.
For a 75 KVA transformer, the total losses at a load level of 40 % should be around 0.8 KW. If the transformer you mention is in good working condition I think you should try to measure this value (let’s make science!).
