ARA interchange rule 30 called for reweighing whenever a car was "materially changed by repair, alterations or repainting". This applied to tank cars even though they were not subject to regular, period reweighing.
It's hard to imagine how repainting a tank car would significantly change the light weight (which was always rounded to nearest 100 lbs), and the Rule 30 language implies some discretion as to what a "material" change in weight might be.
My guess is that reweighing of tank cars were most frequently triggered by a swapping out of the trucks, Until the mid-1920s, all tank cars were delivered with arch-bar or (less commonly) Andrews trucks. These were eventually replaced with CSF trucks, either by rule (arch-bar) or due to owner preference (Andrews).
Other significant alterations likely included the addition of heating coils. In their 1921 All About Tank Cars book, the Standard Tank Car Company indicates that the addition of steam coils added 1000 lbs to the weight of the car.
Conversion from KC or (KD) brakes to ABs is also an alteration that likely changed the light weight. In addition to the changes in hardware and plumbing, alterations to the frame were needed to secure the three components of the AB system.
In some instances, these alterations might have been made concurrently, and perhaps in concert with more subtle "tweaks" to the tank car bodies (e.g., manway covers, safety placard holders, running boards, etc.)
My view is that whether or not a tank had been reweighed depended both on when it was built and when it was photographed. A 1927 AC&F build might not have undergone any significant alterations until the AB brakes were applied, perhaps 25 years later. But a similar car built three years prior would have needed new trucks to comply with the 1940 arch-bar ban. There are many other scenarios that would have dictated exactly when a new light-weight would need to have been stenciled onto the car.
Swall Meadows, CA