Is there an atlas/book with road weight limits?

You will want to examine the bridge in question for a red and white sign near the ground, about the size of a notebook. It will bear the values for a axle loading of a three axle pumper truck fire dept ratings in tandem weight in tons and steer axle weight. Sometimes hook and ladder trailer values are provided along with two axle pumper values.

You literally will find that all bridges in the USA is case by case in weight rating. Interstate bridges have a certain tonnage limits way beyond our pitiful 40 ton. When you get down into say New Haven Connecticut by the water and are confronted by a ten ton drawbridge you cannot cross it. That is where you stop call the Law to come out and assist. They are more than happy to assist you. I have done that several times. Once I encounter a bridge like that either weight or clearance, I make a note of it in the atlas (Rand McNally Motor Carrier Atlas only, laminated plastic pages taking a certain marker. and a notebook containing by state using bible blank tabs for them. To maintain a list of bad shippers, recievers, bridges and so on.)

Nothing computer. Just all paper.

 

This is what you need.
https://www.iowa80.com/pd/rand-mcnally-large-scale-motor-carriers-atlas/227913/

 

If you know the state/county you will be in for questionable roads, you can check the county's road commission website.
A lot have that information. I know, not convenient, but at least something more than waiting until you get there and see the sign.

 

It has more detailed local road info.