Plasmonic nanocavity has been an excellent platform to study light matter interaction under ambient conditions and within sub-diffraction volumes. However, controlled strong light matter interaction in the plasmonic system has rarely been reported. Here, we design a plasmonic tweezers, which can trap a molecular J-aggregates, and be a plasmonic cavity to investigate the strong light matter interaction. We use finite-difference time-domain methods and Maxwell stress tensor to evaluate the optical response and the trapping performance. With the help of coupled oscillator model and virtual excitons theory, we analyze the strong coupling progress in lower excitons system, we further introduce a `coupling force' parameter to characterize the relationship between the optical force and model volume in the coupling system. The proposed method offers a way to locate a molecular J-aggregates in a plasmonic tweezers for investigating optical force performance and strong light matter interaction.