This is a great video with some excellent testing and analysis of BB weights.
If you're an airsoft and physics nerd like me, you'll appreciate it.

https://youtu.be/JtYlIpIq2Xk?si=rC-v5VhBevRNRG4Z

Morale of the story:
A lighter BB will get to the target faster, but bleed of speed quicker, so great for short range engagement.
A heaver BB will get to the target slower, but maintain velocity for longer giving you more range.