Jeff423
US Veteran
You should NEVER touch the cocking notch on a S&W hammer. The cocking notch is only .006/.007 inches high. One nick or boo boo and the hammer is ruined.
If the notch is in good shape, and spring tension isn't behind this, then the trigger sear will need sharpened. That is the part you touch, not the cocking notch. The trigger sear needs to be sharp enough to shave your finger nail in order to operate properly. So again, any nicks or boo boos on the sear and you will get light pulls or push off.
It's not just sharpening - It has to be "sharpened" at the proper angle. There are specific jigs made to do this :Power Custom Series 1 Stoning Fixture Guide
It can be adjusted, within reason, to give heavier or lighter pull weights.
Jeff