A,C, and E seem to be the same weight, B is heavy, D is light, but generally speaking within a class A>B>C>D>E in terms of what they do.
You'd think that the extra weight of B grade gear would make it a poor choice, but not necessarily. My Asp is flying with class B hyperdrives. Despite the weight it's still longer range then when it had a C fitted.
As to why you don't go straight for A grade? I'd have to agree with the point about cost. This is much more noticeable with the larger ships.A 4A fsd on a cobra costs a million credits more than a 4B. For an ASP the difference between a 6A shield and a 6B is 10 million. This isn't pocket change and they are not even close to how much gear costs for the big boys.