Milk solids per kilogram of body weight (BW) is growing in popularity as a measure of dairy cow lactation efficiency. Little is known on the extent of genetic variability that exist in this trait but also the direction and strength of genetic correlations with other performance traits. Such genetic correlations are important to know if producers are to consider actively selecting cows excelling in milk solids per kilogram of BW. The objective of the present study was to use a large data set of commercial Irish dairy cows to quantify the extent of genetic variability in milk solids per kilogram of BW and related traits but also their genetic and phenotypic inter-relationships. Mid-lactation BW and body condition score (BCS), along with 305-d milk solids yield (i.e., fat plus protein yield) were available on 12,413 lactations from 11,062 cows in 85 different commercial dairy herds. (Co)variance components were estimated using repeatability animal linear mixed models. The genetic correlation between milk solids and body weight was only 0.05, which when coupled with the observed large genetic variability in both traits, indicate massive potential to select for both traits in opposite directions. The genetic correlations between both milk solids and BW with BCS; however, need to be considered in any breeding strategy. The genetic standard deviation, heritability, and repeatability of milk solids per kilogram of BW was 0.08, 0.37, and 0.57, respectively. The genetic correlation between milk solids per kilogram of BW with milk solids, BW, and BCS was 0.62, −0.75, and −0.41, respectively. Therefore, based on genetic regression, each increase of 0.10 units in genetic merit for milk solids per kilogram of BW is expected to result in, on average, an increase in 16.1 kg 305-d milk solids yield, a reduction of 25.6 kg of BW and a reduction of 0.05 BCS units (scale of 1-5 where 1 is emaciated). The genetic standard deviation (heritability) for 305-d milk solids yield adjusted phenotypically to a common BW was 27.3 kg (0.22). The genetic correlation between this adjusted milk solids trait with milk solids, BW, and BCS was 0.91, −0.12, and −0.26, respectively. Once also adjusted phenotypically to a common BCS, the genetic standard deviation (heritability) for milk solids adjusted phenotypically to a common BW was 26.8 kg (0.22) where the genetic correlation with milk solids, BW and BCS was 0.91, −0.21, and −0.07, respectively. The genetic standard deviation (heritability) of BW adjusted phenotypically for differences in milk solids was 35.3 kg (0.61), which reduced to 33.2 kg when also phenotypically adjusted for differences in BCS. Results suggest considerable opportunity exists to change milk solids yield independent of BW, and vice versa. The opportunity is reduced slightly once also corrected for differences in BCS. Inter-animal BCS differences should be considered if selection on such metrics is contemplated.