Etymologically, weak sauce was born in Long Beach California circa 1996. It was inspired by the G Love song "My baby got sauce" to which the adjective weak was added and a neologism was born. I used the term intermittently and was surprised when, two years later, I was visiting northern california and heard it used. Since then, it has spread and false claims as to it's origen have been made.
The full usage is now commonly considered passé. Currently, in Long Beach, sauce is an acceptable description of something thats shitty. It is interesting that G Love's "sauce" was a good thing and it has in fact become a polar term.
person A: the food at baja sonora is weak sauce.
person B: it's worse than sauce, that shit had me urinating out my asshole all night.
Person A: I think it's their enchilada sauce (unrelated).