I don’t know that I’ve ever seen it characterized as “doubling down” before when a party to a lawsuit has appealed to a higher court, but here’s Sarah Doiron on WPRI:

Several parents who are challenging the state’s school mask mandate are doubling down on their efforts by appealing a Rhode Island Superior Court judge’s decision last week to uphold it.

As lead plaintiff Richard Southwell suggests, the court did suggest children are being harmed, only finding that the government’s interests were overriding.  However one feels about that balance, it’s a legal question that should be answered, and that requires the highest available court.