The more amps an AC/DC inverter handles, the heavier, larger, and costlier it gets just like any power supply for any device. Grab any two power supplies with different power ratings and weigh them. As to what the weight, size, and cost differences are between a 72 and 48a unit are, I do not know.
My experience agrees with McRat. In the old days power supplies used 60Hz iron transformers. I could measure power or quality with a bathroom scale. If it took two men to pick it up (vs. one man), the power supply was twice as good/powerful because it had twice the iron. This is not true today!
Today's transformers don't use 60Hz. Even the 15kHz power supplies from the CRT TV days disappeared with analog TV. Since the iron mass is the inverse of frequency, and transistors are cheaper than iron, most modern power supplies operate around 1MHz or more. So the new figure of merit is no longer weight, but temperature. The cooler the better. All Tesla on board chargers are liquid cooled.
Since the on board chargers seem to be working, some people might predict that Tesla will use the same charger, but I don't think so. The technology has changed -- yet again.
The insulated gate bipolar transistor, IGBT, was king a few years ago. All modern Tesla cars use IGBTs in all power supplies. That should change. Thanks to Elon Musk and his friend Larry Page, "The Little Box Challenge" is partly responsible for making ultra efficient power supplies a commodity.
The Little Box Challenge
My guess is none of the power systems in the Model 3 will use insulated gate bipolar transistors. The new technologies will shrink the size and weight and raise the efficiency of all power supplies, inverters, converters, regulators. I also predict that two of the suppliers of Model 3 power systems will be
CE+T Power and
Schneider Electric, the winner(s) of "The Little Box Challenge."
I say that 36A is enough for the Model 3. What do you think?