In this paper, we investigate both theoretically and experimentally the influence of the Agarose hydrogel layer thickness on sensitivity of a proposed relative humidity (RH) sensor based on a silica microsphere resonator coated with Agarose hydrogel. The operating principle of the sensor relies on excitation of whispering gallery modes (WGMs) in the coated silica microsphere using the evanescent field of a tapered fiber. A change in the ambient relative humidity is detected by measuring the wavelength shift of the WGMs in the transmission spectrum of the tapered fiber. Using perturbation theory, we analyze the influence of the Agarose coating thickness on the sensitivity of the proposed sensor and compare the results of this analysis with experimental findings for different coating layer thickness. We demonstrate that an increase in the coating layer thickness initially leads to an increase in the sensitivity to RH and reaches saturation at higher values of the Agarose layer thickness. The results of the study are useful for the design and optimization of microsphere sensors parameters to meet a performance specification.