Often used in text messages as form of slang. A mixture of "legit" and "literally", can be used in certain situations on a daily basis when put into context, the term is usually used to emphasise and convince the listener/reader.
When an event or individual is so legit, that the single term "legit" is too commonplace to describe it. Multiple legitly's can be included for added effect.
Man #1: Dude, my wife just gave birth to a son!
Man #2: Nice! What did you guys name him?
Man #1: Perry.
Man #2: THAT'S LEGITLY LEGIT