I think اتاري is a slight modification of this Arabic verbتراءى which means I see that. You might know this verb يرى see. I think if you learn MSA it will be easy to notice this kind of variation between MSA and a dialect. http://www.almaany.com/ar/dict/ar-en/%D8%AA%D8%B1%D8%A7%D8%A1%D9%89/

It's an Egyptian Arabic word (colloquial) we use in the context of "Oh, I figured out" ----- ذنبي: means (my sin or my fault). So, we can translate the sentence to: "Oh, I figured out that love was my sin/my fault".

اتارى = وجدت ان

For me as an Algerian and my language is MSA , When I see this word , It means for me ATARI , a Japanese Video game company.

It could mean a lot of possibilities. however, the most popular is to use it when you figure out some thing was not clear for you. for example: the behavior of your close friend is not as used to be then you know that he is in love. here you can say اتارى just like "aha that's why!!" ذنبى = my guilt