Sweat suits only direct purpose is to do what it says on the packet- make you sweat more and thus lose water weight short term for a weigh in. improved calorific expenditure through the increased temperature is a myth, as the actual thermogenic effect is minimal.

A secondary function that relates directly to competetive fighting, is that sensible use of the suits can aclimatise the wearer to functioning in a slightly dehydrated state for short periods of time. In a combat competition (boxing,mma etc) not much water is actually ingested during round breaks- the odd sip yes, but mostly it is a rinse and spit to get rid of the dry mouth feeling you get from a gum shield. This means that most fighters are dehydrated in later rounds. Sweat suit training can prepare them for this a little.

By far the best thing is to train and eat in such a way that you make weight without having to resort to dehydration. Even with a weigh in the day before a fight, such drastic measures can leave you weak and unable to perform to your best, and if you are weighing in on the day of comp, you would be better to pull out than try dehydrating with no time to replenish.

As with everything in life, short term fixes seldom beat proper diligent preparation.

Use with caution, dehydration can kill you.
Don't let the door hit ya' where the good lord split ya'