TFT backlight control via GPIO
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. (a) A low-side switch. Switch GPIO high to turn on LED. (b) A high-side switch. Switch GPIO low to turn on the LED.

Figure 1 shows how to switch a large load using a transistor. Any small-signal transistor of the right type should do the job.

How it works:

In Figure 1b a small current (3 mA) is pulled through the Q3 base. This causes Q3 to turn on and saturate - effectively making it an on-off switch. The current that passes through Q3 will be determined by the load of R3 and D2.

Normally R1 or R3 value would have to be calculated to limit the current to the correct value. It sounds as though your backlight may already have that internally.