The airline claims EU laws mean it will lose runway slots if it stops flying.
Virgin Atlantic admits it's flying almost empty planes during the coronavirus outbreak so it doesn't have to give up its runway slots.
The airline claims it's being forced to, because the EU hasn't relaxed its "use it or lose it" rules.
The UK government and the industry are urging Brussels to suspend the law so the airline can both save money and cut carbon emissions.
UK Transport Secretary Grant Shapps wrote to the European Commission yesterday, urging it to allow "flexibility and adaptability" in relation to slots.
Aircraft being flown near-empty to keep slots "would be entirely out of step with both the UK's and the European Union's climate commitments", he added.
"Passenger demand for air travel has dramatically fallen due to Covid-19 and in some instances we are being forced to fly almost empty planes or lose our valuable slots," Mr Weiss said.
"Given the almost unprecedented impact on global passenger demand, the UK slot co-ordinator and the European Commission need to now urgently relax the rules for the whole summer. Common sense must prevail," he added.
Tim Alderslade, chief executive of Airlines UK, the industry body representing UK-registered airlines, said: "Carriers are being forced to fly half-empty planes or risk losing that take-off slot in future, seriously affecting their ability to plan ahead"
"It makes no sense whatsoever under these unique and challenging circumstances to force airlines to fly empty aircraft, wasting money and fuel and creating carbon emissions," he said.
"We urgently need a temporary suspension of the rule - as happened during the financial crisis - to allow airlines to respond to demand and use their aircraft efficiently," he added.
