In the beginning......

"There is at present a considerable risk in war damage to bridges from use by vehicles producing a greater load than that for which a bridge has been designed.

To obviate this risk, it has been decided to adopt a system of classification and marking of bridges and of vehicles."

This is how the Canadian Army found out the why and wherefore about bridging markings.  This process started in 1940 as we have seen and continues to this day  when NATO adopted the system after the war.
During the course of the war, the military bridging arm of the Royal Engineers (and the RCE) grew just as the number and size of vehicles grew.

(a) There will be classes numbered 5, 9, 12, 18 and 24

(b) In each case, a number denotes the approximate weight in tons of the vehicles which
            can safely cross each type of bridge.

(c) Each bridge will be marked with a sign-board showing its class.  In addition, sufficient
           road signs similar in design to the '30-m.p.h." Speed limit sign will be supplied to
           classify the route so that traffic can , if necessary, be diverted.
            These signs will be put up at suitable positions approaching road junctions and
            may be some miles from the bridge.

VEHICLES

(a)  Vehicles will be classified and marked according to the equivalent loads which they
            impose on a bridge.  The classes are in multiplicity of one ton, from one ton upwards.
            Vehicles can cross any bridge bearing a classification number with is the same or
            greater than its own classification.  For example, a vehicle of class 12 can cross
            safely any bridge marked 12, 18 or 24.  It cannot cross a bridge marked 5 or 9.

(b)  Trains of vehicles such as a tractor with its gun, or one towing a trailer, will be given a
            double classification.  The upper number will indicate the class of the complete train
            and the lower number which will be in smaller type, the class of the tractor alone.

(c)  In the case of a vehicle towing another in an emergency, the classification of the train will
            be the sum of the individual classifications of the separate vehicles.  A class 9 vehicle
            towing a similar vehicle would therefore have a net classification of 18 and could cross
            any bridge of class 18 or 24.

(d)  Each vehicle will be marked with its classification.  "B" and R.A.S.C. vehicles will be marked
            with a painted disc and "A" vehicles will be painted with a sign similar to that carried by
            "B" and R.A.S.C. vehicles.

(e)  The vehicle sign will be fixed on the off-side between the off-side edge of the radiator and the
             outer edge of the mudguard.   The detail of fixing will vary with the different types of
             vehicles.

6(a)  The bridge sign and the vehicle sign will be of similar design in colour and lettering,
                although of a different size, in order that they will suggest an association of meaning
                to all drivers.

  (b)  They are designed to legible at a distance of 50 yards by day.

  (c)  The signs will be YELLOW with BLACK figures.
 

7.      Engineers will be responsible for classifying all bridges which they erect, and also for
                classifying and marking civil bridges on such traffic routes as the Staff may decide.

8.      The Staff and Provost services are responsible for making plans for the diversion of
                traffic which is too heavy for bridges on main traffic routes and for the necessary
                traffic control.  Such control points may be instituted far from the bridge itself.