Real-time monitoring of distribution grids is essential to handle the complex operation of modern electric systems. One of the main challenges for the deployment of reliable monitoring solutions at the distribution level is the scarcity of measurement instrumentation in the field. Despite the proposal of some approaches to deal with the underdetermined system caused by the low number of meters, existing solutions are not yet able to guarantee a level of simplicity and trustworthiness similar to the one of conventional weighted least squares (WLS) estimators adopted in transmission systems. This article aims at filling this gap by presenting a WLS-based estimator able to work with only very few meters, in scenarios typically considered as unobservable, and without the need to employ pseudo measurements. The proposed method relies on the use of allocation factors and requires only minor modifications with respect to the conventional WLS, thus offering the benefits associated with the use of a well-known and mature state estimation formulation. Simulations performed on an unbalanced IEEE test grid highlight the performance and advantages of the proposed estimator, proving its suitability for the monitoring of poorly instrumented distribution grids.