The birth weight of chickens does not significantly affect the weight at slaughter, while the different growth rate after birth was one of the important reasons for the difference in slaughter weight. Also, the increase in chickens’ postnatal skeletal muscle weight is the main cause of the slaughter weight gain, but which genes are involved in this biological process is still unclear. In this study, by integrating four transcriptome datasets containing chicken muscles at different developmental times or different chicken tissues in public databases, a total of nine candidate genes that may be related to postnatal muscle development in chickens were obtained, including RPL3L, FBP2, ASB4, ASB15, CKMT2, PGAM1, YIPF7, PFKM, and LDHA. One of these candidate genes is RPL3L, whose 42 bp insertion/deletion (indel) mutation significantly correlated with multiple carcass traits in the F2 resource population from Xinghua chickens crossing with White Recessive Rock (WRR) chickens, including live weight, carcass weight, half eviscerated weight, eviscerated weight, breast meat weight, wing weight, leg muscle shear force, and breast muscle shear force. Also, there was a very significant difference between different genotypes of the RPL3L 42 bp indel mutation in these trains. Further experiments showed that RPL3L was highly expressed in chicken skeletal muscle, and its overexpression could promote the proliferation and inhibit the differentiation of chicken myoblasts by regulating ASB4 and ASB15 expression. Our findings demonstrated that the RPL3L 42 bp indel may be one of the molecular markers of chicken weight-related traits.