That whole strong vs skinny I guess. Type of wood is another conderation. I use a lot of oak and mahogany. Starting with a 20mm thick recycled bed headboard, 45mm gives you plenty of meat to go ape with a sanding disk. 40-45mm seems to me to be about the sweet spot for a 3'er if I space the strings at 12-15mm.
I like to use maple. I have a 3 and a 4 string with it and they have held up well.
The harder and thicker (wood) the longer the sustain. If you like narrow necks, but worry about strength, you can employ a "V" profile. Most woods harder that pine are good for simple 3 and 4 string CBGs, especially if you don't take a lot off when you round the back and it you add a fret/finger board.
An interesting experiment. Put a clamp on tuner on the head piece. Watch the meter, as the weight of your thumb or hand contacts the neck, as you are playing. I think you'll find the answer by doing that.
Warning it is a bit scary..on a 3/4 neck.