We demonstrate interrogation of a large-capacity sensor array with nearly identical weak fiber Bragg gratings (FBGs) based on frequency-shifted interferometry (FSI). In contrast to time-division multiplexing, FSI uses continuous-wave light and therefore requires no pulse modulation or high-speed detection/acquisition. FSI utilizes a frequency shifter in the Sagnac interferometer to encode sensor location information into the relative phase between the clock-wise and counter-clockwise propagating lightwaves. Sixty-five weak FBGs with reflectivities in the range of -31 ~-34 dB and with near identical peak reflection wavelengths around 1555 nm at room temperature were interrogated simultaneously. Temperature sensing was conducted and the average measurement accuracy of the peak wavelengths was ± 3.9 pm, corresponding to a temperature resolution of ± 0.4 °C. Our theoretical analysis taking into account of detector noise, fiber loss, and sensor cross-talk noise shows that there exists an optimal reflectivity that maximizes multiplexing capacity. The multiplexing capacity can reach 3000 with the corresponding sensing range of 30 km, when the peak reflectivity of each grating is -40 dB, the sensor separation 10 m and the source power 14 mW. Experimental results and theoretical analysis reveal that FSI has distinct cost and speed advantages in multiplexing large-scale FBG networks.