There isn't an era where basses were generally heavier or lighter - the woods have always been the densities they are, so it's more of a materials choice situation for the differences in weight. I suppose there are times when certain woods were more favored.
To give you an idea about what a difference the wood makes, let's look at my personal Essence bass. It's make with a Cherry body, 7-piece Maple and Purpleheart neck, Kingwood (a type of Rosewood) top. It weights 10.75 pounds. A standard all Maple Essence bass is typically 8.5 pounds.
Series I and II basses are actually much lighter now, but that's because we don't use brass plates anymore. The continuous wood plates weight much less (and look a bit nicer IMO).