Useful uses for the scale just prior or just after training
I can't answer for what people I've never observed have done, but there is at least one legitimate reason for weighing yourself just prior to training:
- Check progress toward weight class in competition conditions (i.e. if I can pass the weight class in full gear I have nothing to worry about at weigh-ins)
- Tracking progress when doing bodyweight exercises
Even though I primarily focus on training for power lifting, I still incorporate certain bodyweight exercises such as push ups, dips, pull ups, etc. For me a set ends when I can't get a another full rep in. If my reps go down, but my weight goes up it might still be a net improvement.
In either case, this number is kept separate from the weight I use for tracking general weight loss. My full gear weight can be up to 10 lbs heavier than my morning weight tracking due to water retention and the weight of the gear. The purpose of weighing myself just prior to training is simply for tracking my training progress--and is particularly important when I do body weight work.
Useful case for weighing yourself multiple times
The process of making weight for a competition sometimes requires dehydrating yourself just long enough to make your weight class. These people have already dieted down using normal means, and the effort to get those last couple pounds off means they have to sweat out or spit out the excess water until they hit the target goal.
During this time, the athlete will be weighing themselves multiple times to see how close to their goal they've become. After the athlete weighs in, they start the process of rehydrating and refeeding themselves so they can be in the best competitive shape (and more than their weigh-in weight by several pounds).
An athlete can reduce as much as 2-3% of their body mass safely using this process, but I've seen cases where it went poorly. A bad rehydration process cost a friend of mine several pounds on the platform as he had diarrhea. Trying to reduce more than your body can handle will require hospitalization to get back to proper health. Below are a few resources that detail the correct way to do this:
There are those that go too far down the path of over-analysis. In that sense, the feedback from the scale is more like an addiction than it is useful feedback. While your weight can change during the course of a workout, it's usually not enough to impact anything. If you see someone getting on the scale several times during the course of a workout, they are most likely doing something very wrong.