How to reduce pig weight variability?

Genetic part of the equation. Birth weight is highly heritable, from the maternal side: some sow families give heavy piglets, others light. Heritable also means repeatable, sorting sows based on first and/or second litter birth weights will definitely create difference in third or later parity. Service sire, father of the piglets has very little to do with birth weight.
Within litter standard deviation is heritable too, at a lower level, but still. Genetic selection can reduce variation in birth weight. Unfortunately there is a high positive correlation between level and variation. Selecting for higher birth weight will give more variation and selection for more uniformity will make pigs lighter. Interesting challenge for breeding companies.

I fully support the proper sorting of piglets based on birth weight and day of birth, there is serious money involved in the proper management of the different groups.

The sources of variation for birth weight and their relative importance varies from species to species. In pigs, the genetic variation is greatest for the maternal effect and not the direct genetic effect. The uterine environment is the largest source of variation. In beef cattle, the direct effect have more genetic variation. In humans, the maternal effect is largest and the sire has little effect. My wife comes from family with long gestation lengths and gestation high sugars. My first son was born 12 lbs 12 ounces. The beef cattle boys ( profs) - posted a sire summary and put my name and EPD for birth weight of 12.75 -- and suggestion I should be culled as a cow killer. Well-- culling decisions of sires must be based on more than 1 offspring our of one dam -- but also in humans the sire has little impact on the birth of the offspring. The exact opposite of cattle. Horses are in between the sire and the dam breed have effects but if small breed large breed reciprocal crosses are made the larger offspring will be out the large dam breed.

Also the much of the economic impact of variation is at the pork processor level. Increased variation in Carcass weight causes increased variation in the cut weights. The distribution of carcass weight with serial marketing of pigs from a barn ( for example 25 % -- then 25% in 10 days and the remainder in 15 days) results in a non-normal distribution carcass weights. If pigs BW's are close to normal - serial cuts from a normal is not normal. We have done simulation and actual data that the accuracy in which pigs are sorted can double the stand deviation in the carcass weights of the pigs delivered. The amount of variation in carcass weight and the distribution of carcass weight is greatly affected by the accuracy in which pigs are sorted for market. Published in "The Professional Animal Scientist- 2016.