...Oh hell someone beat me to it and even has a direct quote from Walt.. Oh well.
I'm not 100% sure but I am PRETTY sure that weapon weights (shields included) does not lower WPP.
The weight and length of a weapon does effect how fast your MOVEMENT speed is though.
Not 100% if that's correct or not but in all the posts about EQUIP WEIGHT and WPP that I've read, weapon weights aren't mentioned to have an effect on your wpp only weights of helmet(x3), gloves(x2), body armor(x1), legs(x1)
On topic, only time I really use shield breakers is on my PA char with full str 10 IF 10 PS atm and he pretty much smashes through them like nothing. Board shields and Huscarls survive for a little bit, the less hit points shields he rips apart with his teeth no need for an axe at all.