Why is a switching type power supply less expensive and lighter than an equivalent linear power supply?
Why A switcher chops the DC into a high frequency square wave, typically 20 kHz to several hundred kHz, before it goes through the transformer. Transformer core size (and the size of the filter inductors and capacitors that follow) is set mostly by the operating frequency: the higher the frequency, the less core material and capacitance needed for the same power. A linear supply must use a bulky iron core transformer running at the 60 Hz line frequency plus large filter capacitors, so it ends up heavier and costlier for the same output.
Watch out The claim about smaller heat sinks gets the cause backwards: switchers do run cooler, but that is because the pass devices operate fully on or fully off with high efficiency, not because the control circuitry draws less current. And a switcher definitely still needs an output filter to smooth the high frequency ripple.
Higher frequency, smaller iron. 60 Hz needs a heavy core; 100 kHz needs a tiny one.