Naturally, the thickness of the slate adds to the cost of the table (sometimes dramatically) and the table's weight. Which is not a consideration that should be diregarded, not only if the table ever needs to be moved (remember that each time it's moved it will need to be "professionally' leveled), but also with regard to the table's actual location in your house. (If it is not installed on the slab in the basement, then you need to take a look at the floor joists that will support the table).
Moreover, best make plans to have the table delivered by professional movers (this is not the sort of job that a couple friends, six-packs, and a truck can do). Bear in mind that professional movers usually surcharge for pool tables--it's that much of a job.
Oh, don’t forget to check that it’s slate in the first place. :)
7/8” is common now in many quality tables. It reduces the weight some without a noticeable difference from the 1” slate.