Marc,
About 3/16 although my only decent pic is of the handle area, if you could see how the fiddleback poped when held in you hand, it was a real rare piece of hickory for me to find, best of all it was thrown out as trash from a cabinet shop. I should have highlighted it with some stain. I think I prefer maple for a backing for this wood though, super thin white oak would be good in my mind as well.
This bow like the last I posted on your thread is well overbuilt, especially with the fiddleback in play. Both bows were spliced at the handle.