In practice, "light" actually means "suitable for two-weapon fighting"
Here's the description of the "light" weapon property from the rules:
Light. A light weapon is small and easy to handle, making it ideal for use when fighting with two weapons.
Ironically, the description doesn't refer to the weapon's weight at all. Rather, it refers to it being "small and easy to handle". Mechanically, the only effect of a weapon being "light" is that this makes the weapon "ideal for use when fighting with two weapons". To see what this means, we refer to the rules on two-weapon fighting:
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
As far as I know, this is the only mechanical impact that "light" has: it allows two-weapon fighting with that weapon. This isn't merely a consequence of being light, it's literally the definition of "light" as a weapon property.