1. ‘Izzarrite’ in the form of a question means ‘Is everything alright’. The appropriate response to this question is ‘Arrite’.
2. ‘Izzarrite’ as general statement means ‘Everything is going to be alright’
Example 1:

Tom: Hey Bob! Izzarrite?
Bob: Arrite Tom!
Example 2: Hey Dave, I know life is hard sometimes, but Izzarrite!

when you're hungover as shit after a spending a night drunk as a skunk

Slang for "It's alright"
It is a philosophy, a feeling, a lifestyle, an expression, a statement! It is for the strong heart; a warrior who can stand up, dust off one's shoulder, face one's Giant(s) and say "it's alright" even in their darkest days.