What are weekly bosses? What makes them be different from other bosses?
There are currently only 3 weekly bosses, and these can be kind of a spoiler if you haven't reached the end of the current story yet: Dvalin, Andrius, and Tartaglia (Childe).
The difference is that they have a chance to drop exclusive boss materials, which are used to level up your talents beyond level 6. Also, you can only do each of them once a week, and each of them costs 60 resin to claim the rewards.