People wear weight lifting belts to support the back by increasing intra abdominal pressure during maximal lifts (as powerlifters do). However, their use by every day exercisers is probably unnecessary. High blood pressure can result, as well as abdominal muscle weakness caused by relying on a belt. So unless they are hiding their stomachs (pretty funny), they are probably not helping themselves.
I agree with both Joanne and Janet. Unless there’s an underlying physical/medical reason for wearing the belt during “non-maximum” lifts, and particularly in the situation that you describe Michael (where the exerciser is using the belt irrespective of what exercise they are doing or body part that’s being worked), then it may be simply cosmetic (e.g. looking cool) or psychological (e.g. thinking it helps).
They probably do themselves more harm than good. I believe there are studies that demonstrate that weight lifting belts actually create more abdominal weakness because their constant use teaches the body to rely on an external device for stabilization.
As other said before, there is a place for them in power lifting, else I would strongly advise against them.
The weight lifting belt is the single most overrated piece of training equipment on the market. You should teach yourself how to contract your abs to maintain postural alignment and produce force with every exercise you do. Wearing a belt robs your body the ability to do this properly which can lead to weakness in one or more areas. It might make a good Halloween prop, but other than that, leave it alone.