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Two weapon fighting has a clause that seems to imply the weapon need not be a melee weapon, if it has the thrown property.
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. If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.
Can you two weapon fight with non melee thrown weapons, such as a net?
Assume that that the attacker has the dual wielder feat.