Many new physics models beyond the Standard Model, motivated by the recent astrophysical anomalies, include the possibility of several new types of light weak-interacting particles. Typical models, such as Next-to-Minimal Supersymmetric Standard Model and Hidden Dark-sector Model, predict the light Higgs and dark bosons, respectively. The masses of these particles are expected to be a few GeV and thus making them accessible at BESIII. BESIII has recently explored the possibility of light Higgs and dark bosons in several decay modes using the data-sets collected at $J/\psi$, $\psi(3686)$ and $\psi(3770)$ resonances. The $J/\psi$ data have further utilized to search for invisible decays of light vector ($V=\omega, \phi$) and pseudo-scalar ($P=\eta, \eta'$) mesons via $J/\psi \to VP$ decays. This report summarizes the recent results of the BESIII experiment on these new physics topics.