The former military Alouette aircraft crashed at Breighton Aerodrome, near Selby, North Yorkshire, on 17 July 2016.
Nigel Feetham, 36, from Hedon, East Yorkshire, died a week later in hospital.
Investigators also noted there was "no technical failure" with the helicopter.
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In its report, the Air Accidents Investigation Branch (AAIB) said the aircraft exceeded the 1,361kg limit by nearly 15kg.
All four passengers suffered head, back, chest and leg injuries when the aircraft crashed to the ground of the former World War Two airfield, which was hosting a 1940s-themed event at the time.
The AAIB said the flight manual for the SE-313B Alouette II helicopter stated if the aircraft was carrying excess weight then it "must be handled 'gently' at higher speeds and shallow approach angles are required".
It also recommended pilots "reduce speed before attempting sharp manoeuvres".
Investigators said the pilot had been "inviting different people for flights during the course of the day".
But for the fatal flight, he agreed to take four passengers he "hadn't originally planned to", which meant the helicopter "exceeded the flight manual limitation for maximum weight".
Witnesses said they heard a "crack" and a "very loud bang" after the aircraft performed several steep manoeuvres. The main rotor blades hit the tail boom before the helicopter crash landed, the AAIB said.
Airfield owner, the Real Aeroplane Company, said the helicopter was visiting the site where private owners of classic aircraft had gathered for the weekend.
A helicopter which crashed leading to the death of the pilot and leaving four men injured was over its weight limit, an investigation found.