This work introduces a new reduced order modeling strategy for real-time state estimation from sparse sensor observations. The method combines variational data assimilation (DA) performed offline with low-dimensional online state estimation based solely on the available observations. Offline, for a training set of parameters, we solve high-fidelity partial differential equations (PDEs) as well as reduced PDE-constrained optimization problems. The resulting DA-corrected solutions are used to construct a reduced approximation space that incorporates both the governing physics and the observational structure. Online, the state is reconstructed by solving a low-dimensional least squares system. The proposed method uses the state-of-the-art Parameterized-Background Data-Weak (PBDW) approach [1] during the offline stage. Yet, it offers substantial computational savings compared to standard PBDW. We derive the mathematical formulation, as well as structural differences with PBDW, and discuss theoretical results related to well-posedness, error estimation, and continuity. Numerical 2D and 3D results are presented to showcase the performance of the proposed method.