Couple questions related to Weight of the Underworld
1) You are correct, the restriction on what it can enchant is Enchant creature, so it can enchant any creature. If it was restricted to just yours for example it would say "Enchant creature you control"

2) Yes. The enchantment will resolve and the next time state based actions are checked the game will see the creature has 0 or less toughness and die. Note this is not the same thing as being destroyed so things like indestructible and regenerate won't save the creature.