Resistive (copper) loss is only part of the picture. A changing magnetic flux also induces swirling eddy currents inside the iron core itself, wasting energy as heat, and the core material also loses energy each cycle to hysteresis as its magnetisation reverses.
The eddy-current loss is cut down by building the core from thin, electrically insulated laminated sheets instead of one solid block, which breaks up the paths available to those swirling currents. Hysteresis loss is reduced by choosing a magnetically "soft" core material with a narrow hysteresis loop, such as silicon steel.
So beyond just thickening the windings, laminating the core and picking a low-hysteresis core material are the key extra ways transformer losses are minimised.