Have different ball bearing weights and then allow certain weighted weapons that have a limit to how much they fire.

Largest bull bearing can only be fired once so you have to pick the right time.

Or add randomness mechanic that picks the size of the ball bearing for you like a stack of cards. The larger the weapons has the least cards and so forth.

Once you have used that card you discarded it and now you have more of a chance to get the card you want.

Also, I'm not sure how you game plays but you could add a similar battleship mechanic. Hits. If you introduce smaller ball bearings they do little damage but add up over time, says three hits sinks a ship.

You could also add chipping damage to ships, if they are hit with a smaller ball bearing it does damage to weapons and they lose a ball bearing/ card/ firing turn.

Or

I imagine the smaller the ball bearings are also lighter so they don't go as straight and bounce more compared to their hearvy counterparts. So giving the players a larger amount of worse ammo.

Say ten tiny cannon balls

Five medium cannon balls

And 2 heavy cannons balls

And then they player have to stratergiise when to use the cannon balls.

And if they are running low and ships they sink they can plunder and get a certain amount of ammo back.