Didn't he sign the papers the day after she found the duffle bag full of money in the closet? I think he was doing it to protect her/the family (plausible deniability and whatnot)
Jesse is my ♥♥♥♥♥
but then he goes he lets Skylar be "the Danny" at the carwash.
And skylar already knew everything about his other life by the time he signed the papers