The creature’s attacks deal half damage. Two kinds of damage that it deals are not affected, however: ongoing damage and damage that isn’t generated by an attack roll.
When a creature is weakened, it can’t exert force as well as normal. Not only physical attacks are affected; the creature’s magical powers are hampered just as much. The creature’s might is diminished in every way, usually as a result of the life-sapping effects of necrotic damage or other deathly magic.
Published in Player's Handbook, page(s) 277, Player's Handbook 3, page(s) 223, Rules Compendium, page(s) 235, Monster Vault: Threats to the Nentir Vale, page(s) 126.