Action observation (AO) is crucial for motor planning, imitation learning, and social interaction, but it is not clear whether and how an action execution-observation network (AEON) processes the effort of others engaged in performing actions. In this functional magnetic resonance imaging (fMRI) study, we used a "squeeze ball" task involving different grip forces to investigate whether AEON activation showed similar patterns when executing the task or observing others performing it. Both in action execution, AE (subjects performed the visuomotor task) and action observation, AO (subjects watched a video of the task being performed by someone else), the fMRI signal was detected in cerebral and cerebellar regions. These responses showed various relationships with force mapping onto specific areas of the sensorimotor and cognitive systems. Conjunction analysis of AE and AO was repeated for the "0th" order and linear and nonlinear responses, and revealed multiple AEON nodes remapping the detection of actions, and also effort, of another person onto the observer's own cerebrocerebellar system. This result implies that the AEON exploits the cerebellum, which is known to process sensorimotor predictions and simulations, performing an internal assessment of forces and integrating information into high-level schemes, providing a crucial substrate for action imitation.