What an interesting term. By Webster it would be sticking your cheek to the gun stock in as permanent a manner as possible. We as shooters though know it means to have good intimate contact between your cheek and the stock. A gun mount then would include good cheek contact throughout the shot sequence.
Many struggle with this simply because the gun does not fit. I also like to make comparisons between a shotgun meant for sport and hunting to a shotgun designed for shooting clay targets. Often youth shooters do not understand why one uses as raised or step rib. While I see all types from no rib to vented ribs, to step and high raised ribs, the idea behind achieving a good cheek weld does indeed lie with the gun and gun fit.
Let me back up and think about how you first mounted a gun or watched someone mount a gun. What we see is the head wants to be upright, but the gun demands the head to move forward and downward to meet the stock. Even worse is when we see a young shooter trying to move their heads back to get a line of sight down the rib and to do this they must lean back and push the gun forward.
Most are aware of the two-finger rule that states your nose should be about 1.5” or two fingers from your nose to either your right or left thumb. This is tough position for first time shooters as to get there as I said they must push their head down and forward. Many will creep or crawl their heads towards this mark to achieve what they hope is a true sight line down the barrel. The finished awkwardness of a good cheek weld is difficult to repeat time after time.
What one really wants is to be able to raise the gun to an upright head position that allows the gun stock to meet the cheek in a manner that is repeatable and really simplified. What we are talking about here is mechanics that can help a shooter hit more targets but is not the catch all for all good or great shooting. With any good gun fit a shooter can relax, raise the gun, square their eyes to the rib and obtain a quality repeatable gun mount that includes a great cheek weld.
The dressing room mirror is an understated way to improve your gun mount and achieve a good cheek weld. In front of the mirror repeat your gun mounts and the sequence that must occur prior to calling “pull”. Let me add here I have also seen cheek welds that resulted in bruising. The violent reaction of the gun upon firing is moving it rearward and into one’s cheek. If the check has an opportunity to release even slightly from the stock, there can be a bounce off the cheek creating discomfort. This is rare and is often reduced with powder or lubrication to allow the stock to slide against the cheek. But bruising most often is from allowing the cheek to move away from the stock and that is simply raising ones head to look around.