BP originally expected to pay $7.8 billion to resolve claims under a 2012 settlement, but by late April it had boosted its estimate to $10.3 billion, according to a regulatory filing.
About $5.13 billion has been paid out so far to 63,597 claimants, according to a website maintained by claims administrator Patrick Juneau.
In its appeal, BP complained that rules adopted by U.S. District Judge Carl Barbier compromised its right to appeal awards he approved and which the company did not like to the 5th Circuit.
Writing for the appeals court, Judge Fortunato Benavides said BP deserved that right to appeal because it did not expressly waive it.
"Where a settlement agreement does not resolve claims itself but instead establishes a mechanism pursuant to which the district court will resolve claims, parties must expressly waive what is otherwise a right to appeal from claim determination decisions by a district court," the judge wrote.
"The point at which a party seeks the district court's discretionary review is the point at which further review by this court becomes a possibility," Benavides added.