The Battle Master fighter's Disarming Attack maneuver can make someone drop a weapon at their feet. The only advantage is if others want to dash away or you need to remove a reaction parry from the opponent before they get their own turn.
When the bad guy's turn comes around, they pick it up (free interaction with an object) and go about their business.
Do I have that right?
To my understanding, you wouldn't be able to use your own free object interaction to pick up and/or throw away their weapon (unless you have movement left over, and you're either two sizes smaller than your opponent or you're a halfling) because the weapon is in the enemy's space – not yours.
Best Answer
There's nothing in the rules to prevent you from interacting with an object in an occupied space (most of the time prohibitions like that in the rules specify held, I think that's a reasonable bar).
Thus you could use your own interact with object free action to pick up their weapon. Though as a DM I may not allow this (since it's more complicated than picking up something in your own space since they may want to contest that). I'd probably make you use an action to pick it up or kick it away (thus it would be up to someone else, or you using your action surge).
That said, there is no prohibition, and picking up a dropped item is a free action. So the most useful thing you can probably do is snatch the weapon up so they can't regain control.