Intubation damaged uvula, swelled up. Four weeks later not back to normal size yet. Anything a doctor can do to help, or simply have to wait?

Get it evaluated . Typically, a traumatized uvula due to intubation would be noticed in the recovery room. Assuming you had verified that it was due to direct trauma with intubation (had anesthesia evaluate in recovery room), this seems like a long time for it to persist. Notify the anesthesia personnel in charge and/or consider an ENT evaluation. .
Mgt. I agree that ENT should evaluate. I would suggest discussing an aerosolized steroid solution to treat the swelling locally. Other considerations include a possible infection of the soft tissues. A culture can be obtained to determine the cause.