A flow balancing valve for a multistage combustor includes a first pressure feedback line, a first burn line, and a first metering port fluidly connected to the first fuel injector. The flow balancing valve further includes a second pressure feedback line, a second burn line, and a second metering port fluidly connected to the second fuel injector. A metering land is located between and defines sizes of the first metering port and the second metering port. An increase in pressure differential between the first pressure feedback line and the second pressure feedback line causes a compensatory movement in the metering land to balance fuel flow for the first fuel injector and the second fuel injector.