"See you later you big fag" is a response to ttyl or "talk to you later". It implies to the person who wrote ttyl that ttyl is a gay thing to write in an email and that you are a fag for writing it. Typically used between guys who feel that any abbreviations are not cool.
Email 1: Guys, we're heading to the party after work tonight, ttyl
Email 2: I'll catch up with you there, sylybf