It looks like a ship's defense strength is not reduced when it is damaged by a weapon that it is weak against.

One specific example was when I had a fleet with 196 attack power in mass drivers (14 small ships each armed with 4 graviton drivers and 20% weapons ability) and used this fleet to attack a single ship with 57 beam defense and 28 hitpoints. I've reloaded and retried this battle several times, and the enemy ship always survives the first round of combat, usually taking just a few points of damage. My ships' damage does not increase during a round, like I would expect if the enemy's defenses were reduced.

Spoilers for the campaign:

This happened in the campaign against dreadlord ships, so maybe this is a special power of theirs. Anyone have this happen against a normal opponent?