Goats with diverse economic phenotypic traits play an important role in animal husbandry. However, the genetic mechanisms underlying complex phenotypic traits are unclear in goats. Genomic studies of variations provided a lens to identify functional genes. The work aimed to search for candidate genes related to body measurements and body weight of Karachai goats and develop an experimental PCR-RV test system for genotyping significant SNPs. Comparison of GWAS results for ages 4 and 8 months revealed 58 common SNPs for significant genotypes. 11 common SNPs were identified for body weight, 4 SNPs—for group of traits withers height, rump height, body length, 2 SNPs—for withers height and rump height, 1 SNP—for body length and chest depth. Structural annotation of genomic regions covering a window of ±0.20 Mb showed the presence of 288 genes; 52 of them had the described functions in accordance with gene ontology. The main molecular functions of proteins encoded by these genes are the regulation of transcription, cell proliferation, angiogenesis, body growth, fatty acid and lipid metabolism, nervous system development, and spermatogenesis. SNPs common to body weight and localized within a window of ±200 kb from the structural genes CRADD, HMGA2, MSRB3, FUT8, MAX, and RAB15 were selected to create a test system. The study of meat productivity after slaughter and chemical analysis of muscle tissue in Karachai goats at the age of 8 months of different genotypes according to the identified SNPs revealed that rs268269710 is the most promising for further research and use in breeding. The GG genotype is associated with a larger live weight of animals, a larger carcass yield, the content of the boneless part in it, and the ratio of protein and adipose tissue in meat preferred for dietary nutrition. These results will contribute to the genetic improvement of Karachai goats.