Is it a 9/10 or a 10/11 rod? I see B&W do two 15 footers in that model.
Looking on the Rio website they have tables with recommended lines but unfortunately your exact model is not listed, however, if the line is 640gr that puts it at the very upper end of B&Ws ratings for their 15 footers, ie, an 10/11 weight line.
Working on that principle, Rio recommend the 10/11 AFS for beginner/improver casters where the extra weight in the line will help load the road during a spey cast. They recommend the 9/10 for casters that can cast well and load a rod easily.
As for the head...none of the head should be in the tip for a clean cast. There is a change in colour in the line and that change should be withing a few inches of the tip ring to start.
I am only starting to get to grips with all these ideas and load ratings etc and experimenting with far too many lines just now!...but I am pretty sure what I have said is correct
I am sure Ben or someone can point you in the right direction though
The Rio spread sheet is fantastic for reference though.