5E has done away with the whole "small long sword" nonsense, when it's basically just a short sword in all aspects. So instead it uses logic. "Heavy" weapons are generally large weapons that are the same size or larger as a medium creature would be, so it would be twice the size or larger than the average small creature, and thus they would have trouble wielding it.
In the old versions they had the world adapt to smaller creatures by giving them a whole set of "small" weapons. But logic dictates that it would make a lot more sense that small creatures would adapt to the world, using the smallest of a regular set of weapons like a medium creature would use medium sized weapons. Which means a Halfling would wield a short sword the way a human would wield a long sword, or a long sword the way a human would wield a great sword.