I use BJansen - Lam Stack Calculator pretty often, I asked him about reducing from 1-3/4" to 1-1/2" and this is what he said.
1/4" narrower limbs = 14% less pounds
47# x 14% = 6.58---47 - 6.58=40.42#
I did this on a recurve and it worked
1/4" =14% so divide 14% by 4 X 3 =10.5 for 3/16"
3/16" narrow should be 10.5% less
47# x 10.5%=4.935----47 - 4.935=42.065#
The hard thing IF you are not a Bowyer is doing it right