I have a friend who has a quality revolver that is in excellent condition and it DOUBLES! Yes you read it right, it doubles. Can anyone figure this anomaly out. One thought is that it has a weak firing pin spring and blows the hammer back.Don't know the exact model or brand but I think it is a Smith and Wesson.

Unless it is the Webley-Fosbery automatic revolver, I think you have already figured it out. Tell him to tighten the mainspring screw.

are the primers pierced..

Smith & Wesson had problems with that occuring on some of their big caliber revolvers. The .500 especially. It's been called an un-intended 'double tap' or 'bump-firing'.

Here's a video that shows one.

S&W got quite a few complaints about the 'problem' especially when the .500 hit the market.

Second video on the link is S&W's R&D to show that the revolver mechanism works as designed and the doubling isn't their problem.

http://www.thefirearmblog.com/.../500-sw-double-taps/

Revolver doubling is usually caused with a hard kicking magnum.
The shooter is not gripping the revolver hard enough, at the first shot, the shooters trigger finger relaxes, allowing the trigger to move foward. As a reaction to the recoil the shooter tightens up his grip, hard, and also pushes the revolver away from his face/head, causing his trigger finger to tighten up also, as in making a fist, and it pulls the trigger a second time.

The solution is to have a hard grip on the revolver before you pull the trigger, and not to relax your grip until after the recoil.