B737 pilot reported stabilizer trim and autothrottle malfunctions. Flight crew returned to departure airport and landed uneventfully.

Narrative

Immediately after departure from ZZZ; the Captain (CA) Pilot Flying (PF) noticed no response while selecting nose down electric stabilizer inputs. PF asked Pilot Monitoring (PM) to attempt nose down electric trim as well to no avail. Both CA and First Officer (FO) controls had no nose down trim capability but electric trim and auto trim did work for nose up inputs. The CA (PF) directed the PM to request a vector from ATC and to maintain 8000 ft. and 250KIAS to establish a controllable flaps up/gear up flight regime. During the climb and level off; it was also determined that the auto-throttles did not respond appropriately to FMC or Mode Control Panel (MCP) speed window inputs. The last correct input from the auto-throttles was upon depressing the TOGA buttons for takeoff where it was apparent that the throttles were essentially in a 'hold' mode. As a result; airspeed reached between 250-260KIAS during the climb prior to recognizing the auto-throttles were also inoperative.Because of workload concerns; initially the CA opted to [request priority handling] while determining the available control ability and choosing the appropriate checklist. Once leveled off and manually trimmed to a straight and level attitude; the flight controls and radios were transferred to the FO as planned during the Pre-Departure briefing. The CA then took the role of PM and handled the stabilizer trim inoperative; overweight landing; and non-routine landing checklists while communicating with Dispatch; Flight Attendants; and Passengers. A flaps 15; overweight (154k GW) landing was executed. We rolled to the end of the runway uneventfully where ZZZ fire and rescue met the aircraft for a hot brakes inspection. With company maintenance concurrence; we decided that there was no concern taxiing under our own power to parking. Brake temperatures were monitored by safety crew and where they continued to follow us to the gate. Recent 737 MAX training with emphasis on trim runaway situations played a substantial role in the safe and expeditious recognition of the aircraft malfunction. As a result; both CA and FO were very well prepared to execute the appropriate checklists without further incident.