A difficult objection is circular reasoning. If all accidents are proven originated because bodies originate, while bodies are proven originated because all their accidents originate, the conclusion has already been assumed in the premises.
An answer must distinguish classes of accidents. If the origination of some accidents, particularly motion and rest, can be established independently, one can argue from them to bodies and only then infer conclusions about other states.
The valid pattern is not to assume universal origination at the outset, but to move from independently supported premises to a broader result.