Why are car batteries still so heavy?
So, obvious answer first:


  why do batteries still weigh 20kg?


Because they're still the same lead-acid batteries. Simple as that. No other technology came near the low cost per Ampere (and ampere-hour) of those, near the reliability and near the ease of handling. 20kg isn't that heavy, if you consider that "fuel economy" still means your average new car carries around dozens of kilogram of "comfort" functionality, and weighs around 1 Mg for the metal parts alone.


  45 years later, car batteries still look the same and weigh the same.


45? More like 120 years... but yeah. We still build bridges out of steel, our concrete has gotten better, but still is essentially concrete, we use Asphalt for roads, copper is still our favourite conductor, the most commonly found amplifier technology in everything that isn't basically low-frequency is a bipolar-transistor based class A/B amplifier, and our refrigerators still aren't based on more efficient means of heat transport, but on compressing more or less dangerous fluids.