I picked up a weapon at a higher level than my current weapon, but it doesn’t seem to be dealing more damage. Why?

The level of a weapon determines two main things:

1. The number of Traits it has.
2. The max value for its three parameters(visible in the Status page of the Wrist Computer)

While a higher level weapon will have a higher max value for its parameters, the actual amount of each parameter will scale depending on Arjun’s Growth Attributes (Resilience, Command, Drive.)

To increase your weapon’s capabilities, it is also important to check which Growth Attribute it scales with, and focus on gaining more of that Attribute.