'Cuz' is not an actual word - it is just a reduced form of the way we sometimes say the word 'because'.
If it feels natural to you, you can SAY 'cuz' whenever you like in informal contexts - it's just an extreme reduction of 'because', where the unstressed first syllable is not pronounced at all.
The written form, cuz or cos or 'cause, should be avoided. Here's where it's appropriate:
- song lyrics, to reflect what is sung and to indicate a single syllable
- film or cartoon captions, to show that the speech is very casual
- catchphrases, titles, slogans etc, to attract attention and to appear casual
It is optional in this context:
- very short messages between friends, to save time and characters
It is not appropriate in any other written contexts. Learners of English often wrongly believe that spellings which imitate speech ( such as cos/cuz, gonna, wanna and so on) are simply informal language that you can write in any context that isn't formal. Please don't make this mistake.