Weaken means the enemy's recovery, attack, and defense will be lowered for a number of turns.

Malady will reduce the enemy's recovery stat, which will reduce its ability to heal.

Monsters can also inflict these effects on you if they have that skill. If your recovery goes to negative, you might not be able to heal at all, even with healing potions. So, pay attention to the icons next to your health bar to see what status the monster has inflicted on you!