There is alot of speculation out there about several skills, and especially BPC. Some say it increases the minimum value of crafted items (on average). What we do know for certain is that it increases all of your engineering-related professional standings. These in turn increase your COS for non-SIB BPs, albiet extrememly slightly. How high your BPC has to get before it makes any appreciable difference is also a matter of some debate.
Personally, I believe that while skilling junk may be the fastest way to get there it may not be the most efficient. I find the Engineering bumps from mining to be far superior to the bumps from crafting dampers, and I tend to profit far more from mining than from skilling dampers. Also, a good career in hunting can fire up your LWT enough to give you 3-4 free levels in your Laser engineer professional standing. From there it is only 6 levels or so to BPC, less if you mine frequently also. Maybe spend a little change of a nice unlimited BP that makes limited items (Breer M1a/M2a, etc) and skill that. At least you can sell the products occasionally for a markup to offset your costs. Or just go the Jester D-1 route if you want to grind as if you were doing dampers.
While it is true that it is much more expensive PER CLICK to skill weapons, keep in mind that the products you recieve have a larger TT value in proportion, as are the size of the skill bumps. By skilling weapons instead of equipment, you may be able to accomplish the same goal for a whole lot less if you shoot things already.
My Weapons man skill is 113. My mech man skill is 560. My laser weapons engineering pro standing is still higher than my mechanical pro standing.
Also, it may be far cheaper in the long run to simply buy an attchment BP with a high QR and just start banging them out since you will already have a max COS anyway. Eventually if you stick with it you will hit BPC anyway just from making the attachments.