Your issue may have more to do with the super short reset of the trigger as opposed to the weight. On the P99 you barely have to let it forward after firing before you can fire again. Many really appreciate this feature. In defensive situations I wouldn't worry as the initial double action pull is heavy enough to avoid accidental discharge.
As someone who owned the P99 since their intro, strayed from it to the Glock, and is now back to the P99as, I agree with Darkstar888 on the short reset. You'll have to learn it;
it is not Glock, nor any other. The transition from DA to the AS trigger is quick, and as DS
suggested, very short.
Why not, after breaking the DA shot, pause for one or two seconds to allow your muscle memory to acclimate to the trigger reset, before squeezing off the second shot...instead, allow your 3rd and 4th shots to become your fast follow ups for your training. When training, slow becomes fast, and your muscle memory will be attuned to the firearm when you press thru the long steady DA break.
Have you tried a different backstrap? That may (or may not) allow you to gain a better control of the trigger. I run my 99AS with the small backstrap, as I want to get my medium mitts around that thing with a grip that allows total control of all functions.
In the case of the abbreviated grip on your P99c, try swapping out the back strap, and dry firing a bit to see if it fits you better.
I love the paddle release. Once I realized your not supposed to use your thumb and started using my middle finger or trigger finger I fell in love with the speed and lack of need to shift my grip.
This is a best kept secret, known to Walther and HK shooters.
Way less re positioning of the shooting and support hands, and, it becomes instinctual, and very fast!
Beware of the baseplates on the Walther mags tho, and have many on hand, as in colder climates, I have found that if they hit the ground just right, they break.
They might contact the earth 999 times, and on the 1000th, crack.
Not all the mags, and may just have been the polymer technology of the early 2000's, and the P99 40 I own. It happened more with the 40 mags from the Gen 1 gun.
Since ditching my Glock 17 and carrying the Walther 99 since late July, I've not had issue 1 with any of the mags for the P99as. They are all factory.