Were you hauling asphalt? The load slip the officer took the weight from, was it current, you just weighed before this incident? If so, I don't see how you can beat it. I'd start by retaining an attorney. What about the sign, is it obstructed or clearly visible? Was this the first time you drove down this street, or perhaps had been using it as a shortcut, and the officer may have seen you before?
My suspicion is that when the officer stopped you, he asked if you weighed, and if you had your scale ticket. You were honest and provided him with your scale ticket. If you didn't have a scale ticket, or had not weighed, he probably would have escorted you to a scale or called a portable scale to weigh you. A real good and expensive attorney might be able to find a loophole there.
From a couple of decades experience as a cop... trying to fight a ticket is fine. They don't mind if you retain the best attorney. Why? Because it will cost as much if not more to try and defeat a good, solid ticket. I've had guys spend up to 4x more than the fine on an attorney, and still lost. The fine amount was reduced, but did he really save anything? There is no such thing as an attorney working for free, ie pro-bono. They're in it for the big bucks.
I don't know what California law is, but it looks like it's going to be a costly oops.