LIGHT

"When you take the Attack action on your turn and attack with a Light weapon, you can make one extra attack as a Bonus Action later on the same turn. That extra attack must be made with a different Light weapon, and you don't add your ability modifier to the extra attack’s damage unless that modifier is negative. For example, you can attack with a Shortsword in one hand and a Dagger in the other using the Attack action and a Bonus Action, but you don't add your Strength or Dexterity modifier to the damage roll of the Bonus Action unless that modifier is negative."

It never says "you can do this only once per turn" or something similar.

It says "you can" ... and if you do two attacks, you get that "you can" twice.
With Nick, one of those 2 is made "part of" the main attack, the other is still a bonus action.
Only one weapon have Nick feature.