Title. Not sure if it is okay or not, but I'd like this to be considered and pointed out why it would be bad.

It would work like this: A weapon with Beast/Slime UV would do more damage against all armors with a piercing defense.
A weapon with Fiend/Undead UV would do more damage against Shadow resisting armors.
A weapon with Construct/Gremlin UV would do more damage against Elemental resisting armors.

Of course, family bonuses from sets like Chroma would apply to this.

It wouldn't have anything to do with damage types, it would just add to the overal damage.
"Low" would give a damage bonus of 1 half pip.
"Medium" would give a damage bonus of 1 pip.
"High" would give a damage bonus of 1 and a half pip.
"Very High" would give a bonus of 2 pips.
"Ultra" (Not sure if it's placed here for family bonuses, apologies if it's not)would give a damage bonus of 2 and a half pips.
"Max" would give a bonus of 3 pips.

Now, to balance it out:
Say, you have a Gran Faust Fiend Medium. It does both normal and shadow, but the normal doesn't matter in this case at all.
Because the UV is a Shadow family, the UV has a penalty of 1 half pip. In process the UV is considered a "Low" UV in Lockdown.