Jenson Button's car was found to be five kilogrammes below the 600kg minimum weight at the San Marino GP.
"The FIA asks the court to exclude the BAR team from the world championship and to fine the team at least one million euros," a FIA statement read.
BAR say they are innocent and have asked the court to dismiss the appeal.
"At no time would I allow anybody in the team to do anything illegal, we have a common culture of integrity and fairness," BAR technical director Geoff Willis insisted.
A lesser penalty could see Button lose the six points he won in Imola.
FIA president Max Mosley said at the start of the season that any team found guilty of cheating would be thrown out of the championship.
FIA officials effectively accused BAR of cheating when claiming: "The team set out deliberately to gain an illegitimate and unfair advantage over other teams."
The FIA believes BAR were using two hidden fuel tanks within the main tank to hide fuel that was used as ballast during the race.
That would allow the car to run lighter than its rivals - and dip below the minimum weight limit in the laps immediately preceding its fuel stop.
It could also be used to allow the team to do more laps before a stop, giving them a strategic advantage in the race.
But the team says the extra tanks are used to pressurise fuel before it is injected into the engine
