The angle of attack for best lift to drag ratio is fixed, so the mathematical background is to resolve a free body diagram
CL(L/D max) = LcosA/½p(V^2)S for glide angle A at best glide speed.
As I'm sure you'll know LcosA approximates L which is approximately W, and then you end up with the expression above.
As a rule of thumb if you know the percentage increase in weight you can work out the percentage increase in speed as half of that, the accuracy however starts to fall away not too far beyond the ratios involved in your examples but give it a shot, it's a useful check for bull$hit in = bull$hit out.