MacBook pro (Early 2011) display backlight won't turn on automatically after waking up from sleep
I would try two things to start with:

Reset the SMC


Shut down your MacBook Pro
Plug in the MagSafe adapter and make sure it is charging
Simultaneously press the shift + alt + control + Power buttons and hold them for about 10 seconds. Let go after that.
Restart your Mac (and move on to the following suggestion):


Reset the PRAM


Press the power button to start up your MacBook Pro
Hold down the following keys:&#8984; + alt + P + R until you hear the start up chime sound twice.
Let go and boot normally.


Test that out and tell us what happens.