Gravitational and inertial effects might be identical, i.e., https://www.linkedin.com/pulse/dark-energy-basis-gravity-warren-frisina-x2poe/?trackingId=2%2FMv9wkTQw6SZ05DUcrytQ%3D%3D
imagine gravitation as a back-flow towards the bary-center of a mass - the speed of this flow is speed-of-light. Thus, if you accelerate the mass, the flow currently focusses at its old location, and will move this focus with delay. The strength of this delay depends on the amount of focusses to be accelerated as a whole, all particles of the mass -> effect of inertia!