In this paper, we present a new parameterization and optimization procedure for minimizing the weight of ribbed plates. The primary goal is to reduce embodied CO2 in concrete floors as part of the effort to diminish the carbon footprint of the construction industry. A coupled plate-beam finite element model and its computational mesh enable simultaneous topology, shape and sizing optimization of ribbed plate systems. Using analytical sensitivity analysis and gradient-based optimization, we achieve significant weight reductions in the range of 24-57%, in comparison to reference designs with regular ribbing patterns. The results strengthen the argument in favor of ribbed plates as a structural system that can serve the environmental goals of the construction industry. While our focus is on ribbed concrete plates in buildings, the proposed mesh-based design parameterization is applicable in the general case of optimizing stiffened shells-with potential contributions also to automotive and aerospace applications. All computer codes used in this study are freely available through a public repository, https://zenodo.org/records/11489996.