The word weak is an adjective, meaning it describes nouns. Weak means that something is without strength or without much power.
Examples:
1. I am weak and cannot arm wrestle my friend.
2. The shelf is too weak to hold all of those books.

Week is a noun. It is a measurement of time. Seven days is one week. Week can also be used in the word weekday. This means any day from Saturday and Sunday.
Examples:
1. I only worked three days this week
2. It's been a long week!