As we all appreciate, curing is an art and not a science. We cannot accurately determine the amount of Nitrite (or Nitrate) that is in the food once the cure has completed without getting it lab tested. What we are doing when we produce a batch of cure (be it dry, immersion or injection) is calculating the
maximum amount of cure that
could remain in the meat once it has been cured. This is called the "Ingoing" or "Added" Nitrite
Just because you weigh out sufficient Nitrite to produce a calculated end concentration of 158 Ppm, the only thing that you can be certain of is that it will actually be less than 158 Ppm. Not all will be absorbed. Some parts of the meat will absorb more than others. Some will be quickly metabolised or chemically broken down. If you heat treat (cook) as part of the curing process then a great proportion of the Nitrite is likely to have gone because of that too. How much less do we have? We cannot tell without expensive laboratory testing. But does it actually matter?
The guidelines (USDA, FSA, European Union etc.) have determined that if we start off with an ingoing level of Nitrite at, say, 158 Ppm then the amount left in the meat after the curing process has been completed will be in the zone where there is sufficient Nitrite remaining for it to provide its protection against anaerobic spores but not be in sufficient levels that will do us harm (or potential harm).
If we were to go to 170 Ppm or even 200 Ppm would that be safe? Yes it would. If we were to drop down to 100 Ppm would that be safe? almost certainly depending on what you are curing. Do we need to add Nitrite in every cure? No we don't. If we are planning on keeping the product refrigerated after curing and will eat it within 10 days then there is often little benefit (other than flavour and colour) from using Nitrite.
Why do we not need to worry about the weight of meat with Pops brine? Pops brine uses an excess of brine and the equilibrium method to distribute it throughout the mass of the meat by diffusion. If we calculate the starting Nitrite concentration in the brine to be 158 Ppm and then add the meat to the brine then water, salts, proteins etc will diffuse in both directions until there is approximately an equal concentration of all of them in both the brine and also the fluids surrounding any intact meat cells. Some may even diffuse or be taken up by intact met cells too. Because the meat is not all water (only about 70-75% water and about 20% protein) we will never get a truly equal weight for weight equilibrium between brine and meat
If you assume 1 Kg of meat and then calculate the theoretical end concentration once equilibrium has been reached using different volumes of brine then it is not until you start to use smaller volumes of brine does the theoretical PPM start to drop off sharply.
With Pops method, providing you have an excess of brine, then the resulting theoretical Ppm will still be within acceptable limits.
If you are using a very small quantity of brine when immersion brining then you do need to take the weight of meat into account.