What is/was the heaviest piloted aeroplane (rigid, non-spaceworthy aircraft) to have ever flown?

The Antonov AN-225 is colloquially named the Dream and bears the NATO designation of "Cossack".

Weighing in at a truly massive 1,420,000 pounds (or 710 tons) the Mriya is the single largest aircraft in the world. It is the heaviest aircraft ever built and has the largest wingspan as well at 290 feet across.

This plane holds the world record for air-lifted single item payload at 559,580 pounds and was originally developed for the transport of the Buran spaceplane.

On the morning of Feb. 24, 2022 Russian forces fought to seize control of the Hostomel Airport, where the AN-225 sat in a hangar. According to War on the Rocks, Russian forces began an attempt to seize control of Kyiv. The Battle of Antonov Airport, or the Battle of Hostomel Airport, began merely hours after President Vladimir Putin announced the start of a special military operation in Ukraine. Russian Airborne forces began an air assault on the airport. The goal was to take control of the city in a matter of days, but the Ukrainian forces fought back.
In the aftermath of the battle, the destroyed AN-225 was shown in pictures online. A press release from Ukroboronprom said it would be restored at the expense of the occupant, meaning Russia.
"The occupiers destroyed the airplane, but they won't be able to destroy our common dream," the Ukroboronprom release said. "Mriya will definitely be reborn. The restoration is estimated to take over 3 bln USD and over 5 years. Our task is to ensure that these costs are covered by the Russian Federation, which has caused intentional damage to Ukraine's aviation and the air cargo sector."
According to FlightRadar24, in November 2022 Antonov announced it had begun work on the new AN-225. The unfinished frame was not damaged in the fighting and assembly will begin after the war.